Optical translation measurement

ABSTRACT

A method for determining the relative motion of a surface with respect to a measurement device comprising:  
     illuminating the surface with incident illumination;  
     detecting illumination reflected from the surface to form at least one detected signal; and  
     determining the amount of relative motion parallel to the surface from said at least one detected signal,  
     characterized in that  
     said determining includes correcting for the effects of relative motion perpendicular to the surface.

FIELD OF THE INVENTION

[0001] The present invention is related to the field of velocity andtranslation measurement and more particularly to methods and apparatusfor the non-contact optical measurement of velocity and translation.

BACKGROUND OF THE INVENTION

[0002] Various optical methods for the measurement of the relativevelocity and/or motion of an object with respect to a measurement systemexist. The kinds of objects and the kinds of motions on which itoperates characterize each method and apparatus.

[0003] The kind of measurable objects may be broadly divided intoseveral groups, including:

[0004] A specially patterned object, for example, a scale.

[0005] A reflecting surface, for example, a mirror.

[0006] A small particle (or few particles), for example precursorparticles or bubbles suspended in fluid.

[0007] An optically contrasting surface, for example, a line or dotpattern.

[0008] An optically diffuse object, for example, blank paper.

[0009] The kind of measurable motions may be broadly divided intoseveral groups, including:

[0010] Axial movement toward or away from the measuring device.

[0011] Transverse (or tangential) motion, where the spacing between themeasuring device and the object is essentially constant.

[0012] Rotational motion, where the object orientation with respect tothe measurement device is changing.

[0013] It is also useful to classify the measurement devices accordingto the number of simultaneously obtainable measurement directions (one,two or three dimensional) and the number of critical components (lightsources, light detectors, lenses, etc.).

[0014] It should be noted that a specific method may be related to morethan one group in the above classification schemes.

[0015] A number of systems capable of non-contact measurement of thetransverse velocity and/or motion of objects using optical means havebeen reported. These methods can include Speckle Velocimetry methods andLaser Doppler Velocimetry methods. Other methods of interest forunderstanding the present invention are Image Velocimetry methods,homodyne/heterodyne Doppler Velocimetry or Interferometry methods andOptical Coherence Tomography (OCT).

[0016] Speckle Velocimetry methods are generally based on the followingoperational principles:

[0017] A coherent light source illuminates the object the motion ofwhich needs to be measured.

[0018] The illuminated object (generally an opaque surface) consists ofmultiple scattering elements, each with its own reflection coefficientand phase shift relative to the other scattering elements.

[0019] The individual reflection coefficients and phase shifts aresubstantially random. At a particular point in space, the electric fieldamplitude of the reflection from the object is the vector sum of thereflections from the illuminated scattering elements, with an additionalphase component that depends on the distance between the point and eachelement.

[0020] The light intensity at a point will be high when contributionsgenerally add in phase and low when they generally add out of phase(i.e., subtract).

[0021] On a planar surface (as opposed to a point), an image of randombright and dark areas is formed since the relative phase retardation ofthe source points depends on the location in the plane. This image iscalled a “speckle image,” composed of bright and dark spots (distinct“speckles”).

[0022] The typical “speckle” size (the typical average or mean distancefor a significant change in intensity) depends primarily on the lightwavelength, on the distance between the object and the speckle imageplane and on the size of the illuminated area.

[0023] If the object moves relative to the plane in which the speckleimage is observed, the speckle image will move as well, at essentiallythe same transverse velocity. (The speckle image will also change sincesome scatterers leave the illuminated area and some enter it).

[0024] The speckle image is passed through a structure comprising aseries of alternating clear and opaque or reflecting lines such that thespeckle image is modulated. This structure is generally a puretransmission grating, and, ideally is placed close to the detector formaximum contrast.

[0025] The detector translates the intensity of the light that passesthrough the structure to an electrical signal, which is a function ofthe intensity (commonly a linear function).

[0026] When the object moves with respect to the measuring device, thespeckle image is modulated by the structure such that the intensity oflight that reach the detector is periodic. The period is proportional tothe line spacing of the structure and inversely proportional to therelative velocity.

[0027] By proper signal analysis, the oscillation frequency can befound, indicating the relative velocity between the object and themeasurement device.

[0028] For these methods high accuracy frequency determination requiresa large detector while high contrast in the signal requires a smalldetector. A paper by Popov & Veselov, entitled “Tangential VelocityMeasurements of Diffuse Objects by Using Modulated Dynamic Speckle”(SPIE 0-8194-2264-9/96), gives a mathematical analysis of the accuracyof speckle velocimetry.

[0029] U.S. Pat. No. 3,432,237 to Flower, el. al. describes a specklevelocimetry measuring system in which either a transmission pattern or apinhole is used to modulate the speckle image. When the pinhole is used,the signal represents the passage of individual speckles across thepinhole.

[0030] U.S. Pat. No. 3,737,233 to Blau et. al. utilizes two detectors inan attempt to solve the problem of directional ambiguity, which existsin many speckle velocimetric measurements. It describes a system havingtwo detectors each with an associated transmission grating. One of thegratings is stationary with respect to its detector and the other moveswith respect to its detector. Based on a comparison of the signalsgenerated by the two detectors, the sign and magnitude of the velocitymay be determined.

[0031] U.S. Pat. No. 3,856,403 to Maughmer, et al. also attempts toavoid the directional ambiguity by providing a moving grating. Itprovides a bias for the velocity measurement by moving the grating at avelocity higher then the maximum expected relative velocity between thesurface and the velocimeter. The frequency shift reduces the effect ofchanges in the total light intensity (DC and low-frequency component),thus increasing the measurement dynamic range and accuracy.

[0032] PCT publication WO 86/06845 to Gardner, et al. describes a systemdesigned to reduce the amplitude of DC and low frequency signalcomponents of the detector signal by subtracting a reference sample ofthe light from the source from the speckle detector signal. Thereference signal is proportional to the total light intensity on thedetector, reducing or eliminating the influence of the total intensityvariations on the measurement.

[0033] This reference signal is described as being generated by using abeam-splitter between the measured surface and the primary detector byusing the grating that is used for the speckle detection also as abeam-splitter (using the transmitted light for the primary detector andthe reflected light for the reference detector) or by using a second setof detectors to provide the reference signal. In one embodimentdescribed in the publication the two signals have the same DC componentand opposite AC components such that the difference signal not onlysubstantially removes the DC (and near DC) components but alsosubstantially increases the AC component.

[0034] In U.S. Pat. No. 4,794,384, Jackson describes a system in which aspeckle pattern reflected from the measured surface is formed on a 2DCCD array. The surface translation in 2 dimensions is found usingelectronic correlation between successive images. He also describes anapplication of his device for use as a “padless optical mouse.”

[0035] Image velocimetry methods measure the velocity of an image acrossthe image plane. The image must include contrasting elements. A linepattern (much like a grating) space-modulates the image, and alight-sensitive detector is measuring the intensity of light that passesthrough the pattern. Thus, a velocity-to-frequency relation is formedbetween the image velocity and the detector AC component. Usually, theline pattern moves with respect to the detector so that the frequency isbiased. Thus, the direction ambiguity is solved and the dynamic rangeexpanded.

[0036] A paper by Li and Aruga, entitled “Velocity Sensing byIllumination with a Laser-Beam Pattern” (Applied Optics, 32, p.2320,1993) describes image velocimetry where the object itself is illuminatedby a periodic line structure (instead of passing its image through sucha pattern). The line pattern is obtained by passing an expanded laserbeam through periodic transmission grating (or line structure).According to the suggested method the object still needs to havecontrasting features.

[0037] There exist a number of differences between Image Velocimetry(IV) and Speckle Velocimetry (SV). In particular, in SV the random imageis forced by the coherent light source, whereas in IV an image withproper contrasting elements is already assumed. Furthermore, in SV thetangential velocity of the object is measured, whereas in IV the angularvelocity is measured (the image velocity in the image plane isproportional to the angular velocity of the line of sight).

[0038] In U.S. Pat. No. 3,511,150 to Whitney et. al., two-dimensionaltranslating of line patterns creates a frequency shift. A singlerotating circular line pattern creates all the necessary translatingline patterns at specific elongated apertures in a circular mask. Thefrequency shift is measured on-line using an additional detectormeasuring a fixed image. The line pattern is divided to two regions,each one adapted for the measurement of different velocity range. Thesystem is basically intended for image motion compensation in order toreduce image blur in aerial photography. Also, it is useful for missilehoming heads.

[0039] U.S. Pat. No. 2,772,479 to Doyle describes an image velocimetrysystem with a frequency offset derived from a grating on a rotatingbelt.

[0040] Laser Doppler Velocimeters generally utilize two laser beamsformed by splitting a single source which interfere at a known position.A light-scattering object that passes through the interfering spacescatters light from both beams to a detector. The detector signalincludes an oscillating element with frequency that depends on theobject velocity. The phenomena can be explained in two ways. Oneexplanation is based on an interference pattern that is formed betweenthe two beams. Thus, in that space the intensity changes periodicallybetween bright and dark planes. An object passing through the planesscatters the light in proportion to the light intensity. Therefore, thedetected light is modulated with frequency proportional to the objectvelocity component perpendicular to the interference planes. A secondexplanation considers that an object passing through the space in whichboth light beams exist, scatters light from both. Each reflection isshifted in frequency due to the Doppler effect. However, the Dopplershift of the two beams is different because of the different angles ofthe incident beams. The two reflections interfere on the detector, suchthat a beat signal is established, with frequency equal to thedifference in the Doppler shift. This difference is thus proportional tothe object velocity component perpendicular to the interference planes.

[0041] It is common to add a frequency offset to one of the beams sothat zero object velocity will result in a non-zero frequencymeasurement. This solves the motion direction ambiguity (caused by theinability to differentiate between positive and negative frequencies)and it greatly increases the dynamic range (sensitivity to lowvelocities) by producing signals far from the DC components. Thefrequency offset also has other advantages related to signalidentification and lock-on.

[0042] U.S. Pat. No. 5,587,785 to Kato, et. al. describes such a system.The frequency offset is implemented by providing a fast linear frequencysweep to the source beam before it is split. The method of splitting issuch that a delay exists between the resulting beams. Since thefrequency is swept, the delay results in a fixed frequency differencebetween the beams.

[0043] Multiple beams with different frequency offsets can be extractedby further splitting the source with additional delays. Each of thesedelays is then used for measuring a different velocity dynamic range.

[0044] A paper by Matsubara, et al., entitled “Simultaneous Measurementof the Velocity and the Displacement of the Moving Rough Surface by aLaser Doppler Velocimeter” (Applied Optics, 36, p. 4516, 1997) presentsa mathematical analysis and simulation results of the measurement of thetransverse velocity of a rough surface using an LDV. It is suggestedthat the displacement along the axial axis can be calculated frommeasurements performed simultaneously by two detectors at differentdistances from the surface.

[0045] In Homodyne/Heterodyne Doppler Measurements, a coherent lightsource is split into two beams. One beam (a “primary” beam) illuminatesan object whose velocity is to be measured. The other beam (a“reference” beam) is reflected from a reference element, usually amirror, which is part of the measurement system. The light reflectedfrom the object and from the reference element are recombined (usuallyby the same beam splitter) and directed to a light-sensitive detector.

[0046] The frequency of the light reflected from the object is shifteddue to the Doppler effect, in proportion to the object velocitycomponent along the bisector between the primary beam and the reflectedbeam. Thus, if the reflected beam coincides with the primary beam, axialmotion is detected.

[0047] The detector is sensitive to the light intensity, i.e.—to thesquare of the electric field. If the electric field received from thereference path on the detector is E₀(t)=E₀ cos(ω₀t+φ₀) and the electricfield received from the object on the detector is E₁(t)=E₁ cos(ω₁t+φ₁),then the detector output signal is proportional to (E₀+E₁)²=E₀ ²+E₀E₁+E₁².

[0048] The first term on the right side of the equation is averaged bythe detector time-constant and results in a DC component. The intensityof the reference beam is generally much stronger than that of the lightreaching the detector from the object, so the last term can usually beneglected. Developing the middle term:

E ₀ E ₁ =E ₀ E ₁ cos(ω₀ t+φ ₀)cos(ω₁ t+φ ₁) =½E ₀ E ₁[cos((ω₀+ω₁)t+φ₀+φ₁)+cos((ω₀−ω₁)t+φ ₀−φ₁)]

[0049] From this equation it is evident that E₀E₁ includes twooscillating terms. One of these terms oscillates at about twice theoptical frequency, and is averaged to zero by the detectortime-constant. The second term oscillates with frequency ω₀-ω₁,i.e.—with the same frequency as the frequency shift due to the Dopplereffect. Thus, the detector output signal contains an oscillatingcomponent with frequency indicative of the measured velocity.

[0050] It is common to add a frequency offset to the reference beam.When such a frequency bias is added, it is termed Heterodyne Detection.

[0051] U.S. Pat. No. 5,588,437 to Byrne, et al. describes a system inwhich a laser light source illuminates a biological tissue. Lightreflected from the skin surface serves as a reference beam for homodynedetection of light that is reflected from blood flowing beneath theskin. Thus, the skin acts as a diffused beam splitter close to themeasured object. An advantage of using the skin as a beam splitter isthat the overall movement of the body does not effect the measurement.Only the relative velocity between the blood and the skin is measured.The arrangement uses two pairs of detectors. Each pair of detectors iscoupled to produce a difference signal. This serves to reduce the DC andlow-frequency components interfering with the measurement. A beamscanning system enables mapping of the two-dimensional blood flow.

[0052] In Optical Coherence Tomography (OCT), a low-coherence lightsource (“white light”) is directed and focused to a volume to besampled. A portion of the light from the source is diverted to areference path using a beam-splitter. The reference path optical lengthis controllable. Light reflected from the source and light from thereference path are recombined using a beam-splitter (conveniently thesame one as used to split the source light). A light-sensitive detectormeasures the intensity of the recombined light. The source coherencelength is very short, so only the light reflected from a small volumecentered at the same optical distance from the source as that of thereference light coherently interferes with the reference light. Otherreflections from the sample volume are not coherent with the referencelight. The reference path length is changed in a linear manner(generally periodically, as in sawtooth waveform). This allows for asampling of the material with depth. In addition, a Doppler frequencyshift is introduced to the measurement, allowing for a clear detectionof the coherently-interfering volume return with a high dynamic range.

[0053] In conventional OCT, a depth profile of the reflection magnitudeis acquired, giving a contrast image of the sampled volume. In moreadvanced OCT, frequency shifts, from the nominal Doppler frequency, aredetected and are related to the magnitude and direction of relativevelocity between the sampled volume (at the coherence range) and themeasurement system.

[0054] U.S. Pat. No. 5,459,570 to Swanson, et al. describes a basic OCTsystem and numerous applications of the system.

[0055] A paper by Izatt et al., entitled “In Vivo Bidirectional ColorDoppler Flow Imaging of Picoliter Blood Volumes Using Optical CoherenceTomography” (Optics Letters 22, p.1439, 1997) describes anoptical-fiber-based OCT with a velocity mapping capability. Anoptical-fiber beam-splitter is used to separate the light paths beforethe reflection from the sample in the primary path and from the mirrorin the reference path and combine the reflections in the oppositedirection.

[0056] A paper by Suhara et al., entitled “Monolithic Integrated-OpticPosition/Displacement Sensor Using Waveguide Gratings and QW-DFB Laser”(IEEE Photon. Technol. Lett. 7 p.1195, 1995) describes a monolithic,fully integrated interferometer, capable of measuring variations in thedistance of a reflecting mirror from the measuring device. The deviceuses a reflecting diffraction element (focusing distributed Braggreflector) in the light path from the source as a combined beam-splitterand local oscillator reflector. Direction detection is achieved by anarrangement that introduces a static phase shift between signals of thedetectors.

[0057] Each of the above referenced patents, patent publications andreferences is incorporated herein by reference.

SUMMARY OF THE INVENTION

[0058] The present invention, in its broadest form, provides an OpticalTranslation Measurement (OTM) method and device, capable of providinginformation indicative of the amount and optionally the direction ofrelative translation between the device and an adjacent object.Preferably, the object is at least partly rough and is closely spacedfrom the device. As used herein, the terms “rough” or “diffuse” meanoptically irregular or non-uniform. In particular, the object may have adiffuse opaque or semi-transparent surface such as a paper. Thisspecification deals mainly with determining the translation or velocityof such diffuse surfaces. However, it should be understood that many ofthe methods of the invention may also be applicable to determination oftranslation of other types of objects such as small scatteringparticles, possibly suspended in fluid. Translation of the object meansthat its rotation in space may be neglected, as explained below.

[0059] In a first aspect of some preferred embodiments thereof, theinvention provides heterodyne or homodyne detection of non-Doppler,non-speckle-image signals derived from changes in the phase and/or theamplitude of reflection from an optically irregular surface.

[0060] In a second aspect of some preferred embodiments thereof,applicable to various methods of motion or velocity detection, theinvention provides a system in which a reflector, which reflects part ofthe incident light, is placed next to the surface whose motion is to bemeasured. The reflector provides a local oscillator signal that isinherently coherent with the light that is reflected from the surface.This aspect of the invention is applicable to both Doppler andnon-Doppler methods of motion detection.

[0061] In a preferred embodiment of the invention, the partial reflectoris a grating and the illumination of the surface whose motion ismeasured pass through the grating. In a preferred embodiment of theinvention, the grating covers a portion of the measured surface and hasa substantial amount of transmission. In this preferred embodiment ofthe invention, the reflections from the surface pass through thegrating. A combination of reflection and partial transmission is oftenuseful, especially in preferred embodiments of the invention whichutilize the third aspect of the invention.

[0062] In a third aspect of some preferred embodiments of the invention,a non-symmetrical transmission pattern is provided to aid in determiningthe direction of motion of the surface.

[0063] In a fourth aspect of some preferred embodiments of theinvention, a phase shift is introduced between at least part of thereflection from the partial reflector and at least part of thereflection from the surface. This phase shift enables the determinationof the direction of motion, increases the dynamic range and improves thesignal-to-noise ratio.

[0064] This phase shift may, in some preferred embodiments of theinvention, be dynamic, i.e., time varying. Such phase variations areconveniently performed by moving the reflector either perpendicularly tothe surface or parallel to the surface or a combination of both. Also,the movement may be of a pattern on the reflector, e.g.—the movement ofa standing wave acting as a grating in a Surface Acoustic Wave (SAW)component. In this respect it is the pattern on the reflector thatmoves, and not the whole reflector. Alternatively, the phase shift isintroduced by periodically varying the optical path length between thereflector and the surface, e.g. by inserting a piezo-electric materialin the optical path.

[0065] The phase shift may also be a static phase shift. Conveniently,this static phase shift is introduced between polarization components ofone of the beams (or a part of the energy in the beam). The direction ofmotion is determined by a measurement of a corresponding phase changebetween detected signals, and more particularly by measurement of thesign of the phase change, between the signals.

[0066] In some preferred embodiments of the invention, which incorporatethis aspect of the invention, a polarizer is utilized to polarize theillumination reflected from the surface. This is especially importantwhen the surface is not polarization preserving.

[0067] A fifth aspect of some preferred embodiments of the inventionprovides for Doppler based detection of motion of a surface in adirection parallel to the surface. In this aspect of the invention, asingle beam may be incident at an angle to the surface or may even beincident perpendicular to the surface.

[0068] A sixth aspect of some preferred embodiments of the inventionprovides for simultaneous two or three dimensional translation detectionusing a single illuminating beam and a single reflector to provide localoscillator reference beams. In a preferred embodiment of the invention,the signal generated by a single detector is used to determine thetranslation in two dimensions.

[0069] In a seventh aspect of some preferred embodiment of theinvention, a spatial filter is provided such that substantially only asingle spatial frequency of the illumination reflected from the surfaceis detected by the detector.

[0070] In some preferred embodiments of the invention, which incorporatethis aspect of the invention, the spatial filter comprises a lens havinga focal point and a pinhole that is placed at the focal point of thelens.

[0071] Preferably, the illumination of the surface is collimated and thespatial filter filters the reflected illumination such that onlyradiation reflected from the surface substantially in a single directionis incident on the detector.

[0072] In an eighth aspect of some preferred embodiments of theinvention the spatial filter is realized by an “effective pinhole.” Thiseffective pinhole is achieved by focusing a local oscillator field, asfor example light reflected or diffracted from a grating, on thedetector. In this way, amplification of the field reflected from thesurface is achieved only at the focus of the local oscillator field.

[0073] Preferred embodiments of the invention, which utilize aneffective pinhole, are easier to align and have looser tolerancerequirements. This is especially true when the local oscillator isderived from light diffracted from a grating at non-zero order since forthis case the placement of the pinhole depends on wavelength. Thus, thewavelength stability requirement of the source of illumination is muchrelaxed when an effective, rather than a physical pinhole is utilized.

[0074] A device, according to a preferred embodiment of the invention,includes a light source, a grating, a spatial filter, a photo-detector,and signal processing electronics. The light source provides at leastpartially coherent radiation, which is directed toward the surface, suchthat part of the illumination is reflected or back diffracted from thegrating towards the detector. An optical grating is placed between thesurface and the light source, preferably close to the surface. The lightreflected from the surface interferes with the light that is reflectedor back diffracted from the grating. The detector signal includes anoscillating component, that is representative of the surface translationrelative to the optical device. The interference may take place with thenormal reflection from the grating or with light diffracted at any ofthe grating orders. Most preferably, the light is spatially filteredprior to detection by the detector. Two dimensional translationmeasurement may be achieved by using two or more detectors illuminatedby orthogonal reflection orders from a two-dimensional grating or byutilizing two separate gratings for the two directions. A thirddimension may be deduced by vector calculation of the translationsmeasured in different orders at the same axis using different signalanalysis techniques on the same signal.

[0075] Optional detection of the direction of translation (as opposed toits absolute magnitude) is preferably achieved by modulating the gratingposition to provide a frequency offset. Alternatively, a varying opticalpath length between the grating and the surface introduces the frequencyoffset. Alternatively, phase shift is introduced between differentpolarization components to provide for direction-dependent phasedifference between corresponding detected signals. Alternatively, thedirection may be determined by other means.

[0076] A ninth aspect of some preferred embodiments of the inventionrelates to alternative methods of determining the direction of motion.In preferred embodiments of the invention which provide this aspect ofthe invention, mechanical motion of an optical part is utilized todetermine the direction of motion. In some preferred embodiments of theinvention, two detectors are provided. Motion in one direction causesillumination of one of the detectors by light reflected or refractedfrom the grating. Motion in the other direction causes illumination ofthe other detector.

[0077] A tenth aspect of some preferred embodiments of the inventionrelates to a method utilizing Doppler shifting of the light reflectedfrom the surface. A local oscillator field is provided by lightreflected from a reflecting surface situated at an angle from the movingsurface. The light reflected from the reflecting surface and the lightreflected from the moving surface interfere on a detector to produce asignal with a frequency proportional to the relative velocity of the twosurfaces. This method has the advantage that no grating is required andthe alignment and frequency stability of the illumination issubstantially uncritical.

[0078] The methods and devices of the invention are applicable to a widerange of applications that require measurement of translation. One suchapplication is a “padless optical mouse”, that can effectively control acursor movement by moving the mouse across an optically diffuse surfacesuch as a paper or a desktop. Another exemplary application for theinvention is for a “touch-point”, that translates finger movement over adevice aperture to control a cursor or any other translation or velocitycontrolled entity.

[0079] In accordance with a preferred embodiment of the invention, themeasurement apparatus comprises a light source for providing at leastpartially coherent radiation. The source radiation is directed toward anoptical one-dimensional or two-dimensional grating, which is preferablyclose to the surface. The light reflections from the grating and fromthe surface interfere, and the light is collected through a spatialfilter (for example, a lens and a pinhole at its focal point) onto alight-detector. The resulting interference signal contains beats relatedto the relative translation of the optical apparatus and the surface. Inpreferred embodiments of the invention, the translation is measureddirectly by counting zero crossings of the oscillating detector signaland is thus not subject to errors caused by velocity changes. Forpreferred embodiments of the invention, substantially instantaneousposition determination is established.

[0080] In many applications the translation direction as well as itsmagnitude is required. In a preferred embodiment of the invention, thisis accomplished by incorporating a dynamic phase shifting device (suchas a piezoelectric transducer) which creates an asymmetric phase shiftpattern (typically a saw-tooth waveform) between the light reflectedfrom the grating and from the surface, enabling simple extraction of thedirection information.

[0081] In another preferred embodiment of the invention, a static phaseshift is introduced between different polarization components of a beamand direction is determined utilizing a resultant phase differencebetween corresponding detected signals.

[0082] Alternatively, direction detection is accomplished by using a,preferably specially designed, asymmetric transmission pattern for thegrating/matrix (such as a saw-tooth transmission or other form asdescribed herein) with appropriate signal processing/manipulation on thedetector output signal. An asymmetric transmission pattern providesmeans for motion direction detection in other velocimetry methods aswell, such as speckle velocimetry. Alternatively, direction detection isprovided by utilizing a mechanically movable element that switches thereflected illumination between detectors, dependent on the direction ofmotion.

[0083] A speckle-free, coherent detection of translation may bedetermined by collecting the scattered light (the light which passesthrough the grating and is reflected from the moving surface) with aspatial filter, such as a combination of a focusing lens and a pinholeaperture (or single mode optical fiber) at the focal position of thelens. The light reflected from the surface is combined with a localoscillator light field (which is preferably the light reflected ordiffracted by the grating itself), which field is preferably a part ofthe light beam that also passes through the spatial filter. Theinterference with the strong local oscillator light source providesamplification of the detected signal by an intensity-sensitivephotodetector. This coherent detection method is termed homodynedetection.

[0084] The spatial filter is operative to spatially integrate lightreflected from the surface to a detector, such that the relative phasesof the reflections from different locations on the surface areessentially unchanged when the surface moves with respect to thedetector. Furthermore, the phase of a scatterer on the surface (asmeasured at the detector) depends linearly on the surface translation.Also, the spatial filter is ideally used to filter the local oscillatorsuch that the detector will integrate over no more than a singleinterference fringe resulting from the interference between the localoscillator and the light reflected from the surface.

[0085] In one extreme case, the light incident on the surface isperfectly collimated (i.e.—it is a plane wave). Thus, the spatial filtermay simply be a lens with a pinhole positioned at its focal point. Anytranslation of the surface does not change the relative phases of thelight integrated by the spatial filter. The local oscillator beam formedby the reflection or the diffraction from the reflector or grating isalso perfectly collimated, so that it can also be passed through thespatial filter (the spatial filter is positioned such that the image ofthe source falls on or within the pinhole). This forces a singleinterference fringe on the detector. No limitations are imposed (withregard to spatial filtering) on the spacing between the reflector andthe surface.

[0086] In another extreme case, the spacing between the surface and thereflector is negligible. This allows for the use of a substantiallynon-collimated incident beam while still maintaining the relative phasesof the reflections from the surface irrespective of it's translation andalso maintaining the same focusing point for the local oscillator andthe reflection from the surface. Optionally, the spatial filter may beimplemented with a lens and a pinhole positioned at the image plane ofthe reflection of the source as a local oscillator.

[0087] In order to have (at most) a single speckle integrated by thedetector, the pinhole size should not exceed the size of about a singlespeckle formed by the reflection from the surface (for this reason, themeasurement may be termed “speckle-free”). Thus, if the detector itselfis small enough, it may serve as an integral part of the spatial filterand a pinhole is not required.

[0088] The preferred conditions of unchanged relative phases and singleinterference fringe with the local oscillator at the detector can befulfilled in a multitude of optically substantially equivalent ways. Inparticular, the requirement may be established using a single converginglens positioned before or after the reflection of the light from thelocal oscillator reflector. Alternatively, the lens and the reflectorcan be combined in a single optical device. Also, a collimating lens maybe positioned between the beam-splitter and the surface (i.e.—only lightto and from the surface pass through this lens).

[0089] Non-ideal spatial filtering (as when the pinhole is too large, orwhen it is out of focus for either the reflection from the surface orthe local oscillator or both), results in deterioration of the signaland possibly the addition of noise to the measurement. The level ofdeterioration depends on the amount and kind of deviation from theideal.

[0090] In a preferred method according to the present invention, boththe surface illumination and the reference light are provided using asingle optical element, preferably a grating. The surface and referencelight share a single optical path through most or all of the opticalelements in the device. Moreover, spatial amplitude and/or phasemodulation, may be imposed on the light reaching the surface by thegrating to provide additional means for measuring the surface'stranslation. In particular, tangential translation can be measured evenfor specular reflection from the grating, where no Doppler shift exists,and identification of the direction of motion can also be achieved.

[0091] In an eleventh aspect of some preferred embodiments of theinvention, an integrated motion detection system provides signals thatare indicative of the amplitude and, optionally, the direction of themotion. In a preferred embodiment of the invention at least some of thecomponents of the motion detection system are mounted on an opticalsubstrate. These components preferably include at least a source ofradiation and an optical element, such as a grating, a reflector or apartial reflector, which generates a local oscillator field from theradiation. Also mounted on the optical substrate is a detector that isilluminated by the local oscillator field and radiation reflected fromthe surface whose relative motion is measured. In this embodiment of theinvention, the path lengths of the local oscillator field and the fieldreflected from the surface whose motion is measured is such that the twofields are coherent at the detector.

[0092] In a twelfth aspect of some preferred embodiments of theinvention, accurate measurement of motion parallel to the surface isobtained by compensation of the influence of motion perpendicular to thesurface and compensation of the influence of tilting of the measurementdevice. This aspect of the invention is especially useful for use in acomputer control device such as a computer mouse.

[0093] There is thus provided, in accordance with a preferred embodimentof the invention, a method for determining the relative motion of asurface with respect to a measurement device comprising:

[0094] illuminating the surface with incident illumination;

[0095] detecting illumination reflected from the surface to form atleast one detected signal; and

[0096] determining the amount of relative motion parallel to the surfacefrom said at least one detected signal,

[0097] characterized in that

[0098] said determining includes correcting for the effects of relativemotion perpendicular to the surface.

[0099] Preferably, said at least one signal comprises at least twosignals, at least one first signal which is affected by relative motionparallel to the surface and relative motion perpendicular to the surfaceand at least one second signal which is affected at least by motionperpendicular to the surface, and

[0100] determining comprises determining the amount of relative motionparallel to the surface from the two signals.

[0101] Preferably, determining comprises:

[0102] determining a first amount of relative motion from at least oneof said two signals, said first amount of relative motion including acomponent parallel to the surface and a component perpendicular to thesurface;

[0103] determining a second amount of relative motion from at least oneof said two signals, said second amount of relative motion including acomponent perpendicular to the surface; and

[0104] determining the amount of relative motion parallel to the surfaceresponsive to the first and second determined amounts of relativemotion.

[0105] Preferably, the second amount of relative motion does not includea component parallel to the surface.

[0106] Preferably, the second amount of relative motion includes acomponent parallel to the surface.

[0107] In a preferred embodiment of the invention, relative motionperpendicular to the surface is determined based on a Doppler shift ofthe reflected illumination.

[0108] In a preferred embodiment of the invention, determining comprisesdetermining the amount of relative motion parallel to the surfacedirectly from the two signals without determining the amount of relativemotion perpendicular to the surface. Preferably, the at least one secondsignal is substantially determined by relative motion perpendicular tothe surface.

[0109] In a preferred embodiment of the invention, the at least onesecond signal is a signal based on a Doppler shift.

[0110] Preferably, the at least one second signal is responsive torelative motion parallel to the surface.

[0111] In a preferred embodiment of the invention, the method includesdetermining the amount of relative motion perpendicular to the surface.

[0112] In a preferred embodiment of the invention, determining theamount of relative motion parallel to the surface includes determiningthe amount of relative motion along two non-colinear directions.

[0113] In a preferred embodiment of the invention, the illumination isperpendicularly incident on the surface.

[0114] In a preferred embodiment of the invention, detecting comprisescoherently detecting. Preferably, the method includes reflecting ordiffracting a portion of the illumination from an object, which is partof the measurement device, to act as a local oscillator. Preferably, theobject is a partially reflecting object through which either theincident or reflected illumination passes. Preferably, both the incidentand reflected illumination pass through the object.

[0115] In a preferred embodiment of the invention the object is adjacentto the surface.

[0116] In a preferred embodiment of the invention, the surface is in thenear field of the object. Alternatively, the surface is outside the nearfield of the grating.

[0117] In a preferred embodiment of the invention, the object is agrating. Preferably, the grating produces essentially only a singleorder of transmitted illumination that illuminates the surface.

[0118] Preferably, the illumination is at least partially coherent andthe object is placed within the coherence length of the illuminationfrom the surface.

[0119] In a preferred embodiment of the invention, the local oscillatorillumination and the reflected illumination are incident on at least onedetector to produce said signals and the local oscillator illuminationand the reflected illumination are at least partly coherent at thedetector.

[0120] There is further provided, in accordance with a preferredembodiment of the invention, apparatus for measuring relative motionbetween the apparatus and a surface comprising:

[0121] an illumination source, which transmits illumination toilluminate the surface;

[0122] a first detector which receives illumination from the source,reflected from the surface;

[0123] an object which reflects a portion of the illumination to saidfirst detector, such that the detector generates a first signal based oncoherent detection of the illumination reflected from the surface withthe illumination reflected by the object as a local oscillator;

[0124] a second detector which receives illumination from the sourcewithout receiving illumination reflected from the surface and generatesa second signal responsive thereto;

[0125] a signal corrector that adjusts the first signal for changes inthe intensity of the illumination, based on the second signal; and

[0126] a motion calculator that calculates the relative motionresponsive to the signal from the signal corrector.

[0127] Preferably, the illumination from the source received by thesecond detector is illumination reflected from or diffracted by theobject.

[0128] Preferably, the signal corrector corrects the first signal for aconstant term based on the second signal. Preferably, the signalcorrector includes a difference amplifier that receives the first signaland subtracts the second signal from it to produce an adjusted firstsignal. Preferably, the signal corrector includes a normalizer thatreceives the adjusted first signal and normalizes it with respect to thesecond signal.

[0129] In a preferred embodiment of the invention, the apparatusincludes:

[0130] a third detector that receives illumination reflected from thesurface without receiving substantial illumination from the object orfrom the source and produces a third signal in response thereto, and

[0131] the signal corrector corrects the adjusted signal based on thethird signal.

[0132] There is further provided, in accordance with a preferredembodiment of the invention, apparatus for measuring relative motionbetween the apparatus and a surface comprising:

[0133] an illumination source, which transmits illumination toilluminate the surface;

[0134] a first detector which receives illumination from the source,reflected from the surface;

[0135] an object which reflects a portion of the illumination to thefirst detector, such that the detector generates a first signal based oncoherent detection of the illumination reflected from the surface withthe illumination reflected by the object as a local oscillator;

[0136] a second detector which receives illumination from the sourcewithout receiving illumination reflected from the surface and generatesa second signal responsive thereto;

[0137] a signal corrector that reduces the first signal by an amountproportional to the second signal; and

[0138] a motion calculator that calculates the relative motionresponsive to the signal from the signal corrector.

[0139] Preferably, the illumination from the source received by thesecond detector is illumination reflected from or diffracted by theobject.

[0140] In a preferred embodiment of the invention, the signal correctorincludes a normalizer that adjusts the first signal for changes in theintensity of the illumination, based on the second signal.

[0141] In a preferred embodiment of the invention the apparatusincludes:

[0142] a third detector that receives illumination reflected from thesurface without receiving substantial illumination from the object orfrom the source and produces a third signal in response thereto, and

[0143] the signal corrector corrects the adjusted signal based on thethird signal.

[0144] There is further provided, in accordance with a preferredembodiment of the invention, apparatus for measuring relative motionbetween the apparatus and a surface comprising:

[0145] an illumination source, which transmits illumination toilluminate the surface;

[0146] a first detector which receives illumination from the source,reflected from the surface;

[0147] an object which reflects a portion of the illumination to saidfirst detector, such that the detector generates a first signal based oncoherent detection of the illumination reflected from the surface withthe illumination reflected by the object as a local oscillator;

[0148] a second detector that receives illumination reflected from thesurface without receiving substantial illumination from the object orfrom the source and produces a second signal in response thereto,

[0149] a signal corrector that reduces the first signal by an amountproportional to the second signal; and

[0150] a motion calculator that calculates the relative motionresponsive to the signal from the signal corrector.

[0151] In a preferred embodiment of the invention, the object ispartially transmitting and the object is placed between the illuminationsource and the surface such that illumination of the surface passesthrough the object.

[0152] In a preferred embodiment of the invention, the illumination hasa coherence length and the object and the surface as situated withinsaid coherence length.

[0153] In a preferred embodiment of the invention, the object is agrating. Preferably, the grating produces essentially only a singleorder of transmitted illumination that illuminates the surface.Preferably, the surface is within the near field of the grating.Alternatively, the surface is outside the near field of the grating.

[0154] In a preferred embodiment of the invention, the illuminationreflected from the surface and the illumination reflected by the objectare at least partly coherent at the first detector.

[0155] There is further provided, in accordance with a preferredembodiment of the invention, a method for determining the relativemotion of a surface with respect to a measurement device, comprising:

[0156] illuminating the surface with incident illumination such that theillumination is reflected from portions of the surface;

[0157] coherently detecting the illumination reflected from the surfaceutilizing illumination derived from said incident illumination that wasnot reflected by the surface as a local oscillator, to form at least twosignals;

[0158] determining the magnitude of relative motion of the surface fromat least one of the two signals;

[0159] varying the phase of at least part of the local oscillatorillumination with respect to at least part of the illumination reflectedby the surface; and

[0160] determining the direction of relative motion parallel to thesurface based on a characteristic of the signals caused by said variedrelative phase.

[0161] Preferably, the local oscillator illumination is generated byreflection or refraction of incident illumination from an object that isa part of the measurement device. Preferably, the object is adjacent tothe surface. Preferably, the illumination has a coherence length and theobject and the surface are situated within said coherence length.Preferably, the object is a grating. Preferably, the grating producesessentially only a single order of transmitted illumination thatilluminates the surface. Preferably, the surface is placed within thenear field of the grating. Alternatively, the surface is placed outsidethe near field of the grating.

[0162] In a preferred embodiment of the invention, varying the phasecomprises introducing a static phase change and determining thedirection of relative motion comprises determining the direction ofrelative motion based on a characteristic of the signal caused by saidstatic phase change.

[0163] In a preferred embodiment of the invention, the method includes:

[0164] dividing the illumination that is reflected from the surface intoa first illumination having a first phase and a second illuminationhaving a second phase.

[0165] Preferably, the first illumination and the second illuminationhave different polarizations.

[0166] Preferably, dividing comprises passing the illumination incidenton the surface through a birefringent material. Alternatively oradditionally, dividing comprises passing the illumination reflected fromthe surface through a birefringent material. Preferably, the methodincludes placing a birefringent material between the object and thesurface.

[0167] In a preferred embodiment of the invention, placing thebirefringent material between the object and the surface is operative tocause detected illumination to pass through the birefringent materialtwice.

[0168] In a preferred embodiment of the invention, the method includesdetermining the magnitude and direction of the translation utilizing twodetectors which produce different detected signals depending on thedirection of the translation. Preferably, determining the direction oftranslation comprises determining the direction from the sign of thephase difference between the different detected signals.

[0169] Preferably, the method includes linearly polarizing illuminationreflected from the surface.

[0170] There is further provided, in accordance with a preferredembodiment of the invention, apparatus for determining translation of asurface relative to the apparatus, comprising:

[0171] an optical block;

[0172] a detector, which produces a signal responsive to light impingingthereon, attached to the optical block; and

[0173] a source of illumination that produces illumination, a portion ofwhich passes through the block is reflected by the surface and impingeson the detector after passing through the optical block; and

[0174] circuitry that computes the magnitude of the translation parallelto the surface, responsive to the signal.

[0175] Preferably, the apparatus includes an object within or on thesurface of the block which reflects or diffracts a part of theillumination to the detector without said part impinging the surface,said part acting as a local oscillator for synchronous detection of thereflected illumination by the detector.

[0176] There is further provided, in accordance with a preferredembodiment of the invention, a method for determining the relativemotion of a surface with respect to a measurement device, comprising:

[0177] illuminating the surface with incident radiation such that theillumination is reflected from a portion of the surface;

[0178] detecting at least a first part of the illumination reflectedfrom the surface to form a first detected signal;

[0179] detecting at least a second part of the illumination reflectedfrom the surface to form a second detected signal; and

[0180] determining the amount of relative motion based on a Dopplershift of the reflected radiation, wherein the first and second signalsare in phase quadrature and the detection comprises quadraturedetection.

[0181] Preferably, the method includes detecting the direction ofrelative motion responsive to said first and second signals.

[0182] Preferably, the method includes determining the relative motionin two non-colinear directions parallel to the surface.

[0183] Preferably, the method includes determining the relative motionin a direction perpendicular to the surface.

[0184] Preferably, the method includes determining the relative motioncomprises counting zero crossings of at least one of said first andsecond signals.

[0185] Preferably, detecting comprises coherent detection.

[0186] There is further provided, in accordance with a preferredembodiment of the invention, a method for determining the relativemotion of a surface with respect to a measurement device, comprising:

[0187] illuminating the surface with incident illumination such that theillumination is reflected from portions of the surface;

[0188] coherently detecting the illumination reflected from the surfaceusing a detector, to form a signal;

[0189] utilizing illumination derived from said incident illuminationthat was not reflected by the surface as a local oscillator, for saidcoherent detection; and

[0190] determining the magnitude of relative motion of the surface fromthe signal;

[0191] characterized in that the local oscillator is focused onto asmall area of the detector, such that essentially only a single spatialfrequency of the reflected illumination forms an interference field withsaid local oscillator on the detector.

[0192] There is further provided, in accordance with a preferredembodiment of the invention, apparatus for determining the relativemotion of a surface with respect to the apparatus, comprising:

[0193] a housing having an aperture formed therein;

[0194] a detector within the housing that produces a signal utilized todetermine the relative motion;

[0195] a source of laser illumination of a given wavelength, within thehousing, that illuminates the surface through the aperture, such thatillumination is reflected from the surface via the aperture to thedetector; and

[0196] a filter covering the aperture that passes the given wavelengthwhile blocking light at other wavelengths to which the detector issensitive.

[0197] There is further provided, in accordance with a preferredembodiment of the invention, apparatus for determining the relativemotion of a surface with respect to the apparatus, comprising:

[0198] a housing having an aperture formed therein;

[0199] a detector within the housing that produces a signal utilized todetermine the relative motion;

[0200] a source of laser illumination of a given wavelength, within thehousing, that illuminates the surface through the aperture, such thatillumination is reflected from the surface via the aperture to thedetector;

[0201] a second detector within the housing that receives illuminationreflected from the surface; and

[0202] circuitry that turns off the illumination source whenillumination received by the second detector falls below a threshold.

[0203] Preferably, the circuitry is operative to periodically turn onthe source and to turn it off if illumination received by the seconddetector is below the threshold.

[0204] Preferably, the aperture is covered by a filter that passes thegiven wavelength while blocking light at other wavelengths to which thefirst and second detectors is sensitive.

[0205] In a preferred embodiment of the invention, a part of theillumination to the detector illuminates the detector, without said partfirst impinging the surface, said part acting as a local oscillator forcoherent detection of the reflected illumination by the detector.

[0206] In a preferred embodiment of the invention, the reflectedillumination is Doppler shifted, by said translation, with respect tothe illumination produced by the source and said Doppler shift isutilized in determining the motion.

[0207] There is further provided, in accordance with a preferredembodiment of the invention, apparatus for measuring relative motionbetween the apparatus and a surface comprising:

[0208] an illumination source, which is used to illuminate the surface;

[0209] a detector which receives illumination from the source, reflectedfrom the surface and which receives a portion of the illuminationwithout said portion being reflected by the surface, such that thedetector generates a signal based on coherent detection of theillumination reflected from the surface with the portion of theillumination as a local oscillator, wherein said signal has a frequencyrelated to a rate of relative movement; and

[0210] a motion calculator that calculates the amount of relative motionresponsive to a count of zero crossings of the signal.

[0211] Preferably, the detector includes and including a high passfilter that filters the detector output to form said signal. Preferably,the high pass filter has a slope of less than about 20 dB/octave.Preferably, the high pass filter has a break point at a frequencycorresponding to a rate of movement of less than about 0.5 mm/sec.

[0212] Preferably, the apparatus includes:

[0213] a second detector that detects at least a second part of theillumination reflected from the surface to form a second detected signalutilizing coherent detection, and

[0214] the motion detector determines the amount of relative motionbased on a Doppler shift of the reflected radiation, wherein the signaland second detected signal are in phase quadrature and the detectioncomprises quadrature detection.

[0215] There is further provided, in accordance with a preferredembodiment of the invention, apparatus for determining the relativemotion of a surface with respect to the apparatus, comprising:

[0216] a housing having an aperture formed therein;

[0217] a detector within the housing that produces a signal utilized indetermining the relative motion is determined;

[0218] a source of laser illumination of a given wavelength, within thehousing, that illuminates the surface through the aperture, such thatillumination is reflected from the surface via the aperture to thedetector; and

[0219] circuitry that turns off the illumination source whenillumination received by the detector from the surface is below athreshold.

[0220] Preferably, the circuitry is operative to periodically turn onthe source and to turn it off if illumination received by the detectorfrom the surface.

[0221] There is further provided, in accordance with a preferredembodiment of the invention, a method for determining the relativemotion of a surface with respect to a measurement device, comprising:

[0222] placing a partially transmitting object as part of the measuringdevice, adjacent to the surface;

[0223] illuminating the surface with incident illumination such that theillumination is reflected from portions of the surface, wherein at leastpart of at least one of the incident and reflected illumination passesthrough the object;

[0224] detecting the illumination reflected from the surface, togenerate a detected signal, wherein the object and the surface aresituated within a distance that is less than the coherence length of thedetected illumination; and

[0225] determining the relative motion of the surface parallel to thesurface, from the detected signal.

[0226] Preferably, the transmission of the object is spatially varying.

[0227] In a preferred embodiment of the invention, the object ispartially reflecting and part of the incident illumination is reflectedor diffracted by the object, as a reference illumination and detectionof the illumination is coherent, utilizing said reference illumination.

[0228] There is further provided, in accordance with a preferredembodiment of the invention, a method for determining the relativemotion of a surface with respect to a measurement device comprising:

[0229] placing a partially reflecting object, which is part of themeasuring device, adjacent to the surface;

[0230] illuminating the object with incident illumination such that partof the incident illumination is reflected or diffracted by the object,as a reference illumination and part is reflected from the surface;

[0231] coherently detecting the illumination reflected from the surfaceutilizing the reference illumination, to generate a detected signal; and

[0232] determining the relative motion of the surface parallel to thesurface, from the detected signal.

[0233] In a preferred embodiment of the invention, the object is apartially transmitting object and at least part of at least one of theincident and reflected illumination passes through the object.

[0234] Preferably, the reflection of the object is spatially varying.Preferably, spatially varying comprises periodic spatial variation.

[0235] In a preferred embodiment of the invention, placing an objectadjacent to the surface comprises placing a grating adjacent to thesurface. Preferably, placing a grating adjacent to the surface comprisesplacing the grating sufficiently close to the surface such that thesurface is in the near field of the grating. Alternatively, placing agrating adjacent to the surface comprises placing the gratingsufficiently far from the surface such that the surface is outside thenear field of the grating.

[0236] In a preferred embodiment of the invention, the detectedillumination is at least partly coherent.

[0237] There is further provided, in accordance with a preferredembodiment of the invention, a method for determining the relativemotion of a surface with respect to a measurement device comprising:

[0238] placing a grating, which is part of the measuring device,adjacent to the surface;

[0239] illuminating the grating with incident illumination such that atleast part of the illumination is incident on and reflected from thesurface, wherein at least one of the incident and reflected illuminationpasses through the grating;

[0240] detecting the illumination reflected from the surface utilizingthe reference illumination;

[0241] generating a signal in response to the reflected illumination;and

[0242] determining the relative motion of the surface parallel to thesurface, from the detected signal,

[0243] wherein the surface is in the near field of the grating.

[0244] Preferably, the illumination reflected from the surface isfrequency shifted from that of the illumination reflected from ordiffracted by the object and determining the motion comprisesdetermining the motion based on the frequency shift.

[0245] Preferably, determining the motion comprises determiningvariations in the amplitude of the signal with position. Preferably, themotion is determined from zero crossings of the detected signal.

[0246] In a preferred embodiment of the invention, the object has atransmission characteristic that is spatially non-symmetric. Preferably,the method includes determining the direction of the relative motionbased on a characteristic of the signal caused by said non-symmetry.

[0247] There is further provided, in accordance with a preferredembodiment of the invention, a method for determining the relativemotion of a surface with respect to a measurement device comprising:

[0248] placing a partially transmitting object, which is part of themeasuring device, adjacent to the surface;

[0249] illuminating the surface with incident illumination, which doesnot constitute an interference pattern, such that the illumination isreflected from portions of the surface, wherein at least part of atleast one of the incident and reflected illumination passes through theobject;

[0250] detecting the illumination reflected from the surface, andgenerating a detected signal; and

[0251] determining the relative motion of the surface parallel to thesurface, from the detected signal.

[0252] Preferably, the method includes varying the phase betweenillumination reflected from or diffracted by the object and at least aportion of the illumination reflected from the surface.

[0253] There is further provided, in accordance with a preferredembodiment of the invention, a method for determining the relativemotion of a surface with respect to a measurement device comprising:

[0254] illuminating the surface with incident illumination such thatillumination is reflected from portions of the surface;

[0255] placing a partially reflecting object, which is part of themeasuring device, adjacent to the surface, wherein part of the incidentillumination is reflected or diffracted by the object, as a referenceillumination;

[0256] coherently detecting the illumination reflected from the surface,utilizing the illumination reflected from or diffracted by the object asa local oscillator, to form a signal;

[0257] determining the relative motion of the surface from the signal;

[0258] varying the phase of at least a part of the illuminationreflected from or diffracted by the object with respect to at least apart of that reflected from the surface; and

[0259] determining the direction of relative motion parallel to thesurface based on a characteristic of the signal caused by said variedrelative phase.

[0260] Preferably, placing a reflector adjacent to the surface comprisesplacing a grating adjacent to the surface.

[0261] In a preferred embodiment of the invention, varying the phasecomprises periodically varying the phase.

[0262] Preferably, determining the direction of relative motioncomprises determining the direction of relative motion based on acharacteristic of the signal caused by said periodically varyingrelative phase.

[0263] In a preferred embodiment of the invention, varying the phasecomprises causing the object to move periodically substantially in thedirection of the motion being measured.

[0264] In a preferred embodiment of the invention, varying the phasecomprises causing the object to move periodically substantiallyperpendicularly to the direction of the motion being measured.

[0265] In a preferred embodiment of the invention, varying the phasecomprises:

[0266] providing a transparent material between the object and thesurface; and

[0267] electrifying the material such that its optical length in thedirection of the illumination varies.

[0268] Preferably, the transparent material is a piezoelectric material.

[0269] Preferably, the method includes determining both the magnitudeand direction of the translation utilizing a single detector.

[0270] In a preferred embodiment of the invention, varying the phasecomprises, introducing a static phase change and determining thedirection of relative motion comprises determining the direction ofrelative motion based on a characteristic of the signal caused by saidphase change.

[0271] Preferably, the method includes dividing at least part of theillumination that is reflected from the surface into at least a firstillumination having a first phase and a second illumination having asecond phase. Preferably, the first and second illuminations havedifferent polarizations. Preferably, dividing comprises passing theillumination incident on the surface through a birefringent material.Preferably, the method includes passing the illumination reflected fromthe surface through a birefringent material. Preferably, the methodincludes placing the birefringent material between the object and thesurface.

[0272] In a preferred embodiment of the invention, the method includesdetermining the magnitude and direction of the translation utilizing twodetectors which produce different detected signals depending on thedirection of the translation.

[0273] Preferably, the method includes determining the direction oftranslation from the sign of a phase difference between the differentdetected signals.

[0274] There is further provided, in accordance with a preferredembodiment of the invention, a method for determining the relativemotion of a surface with respect to a measurement device comprising:

[0275] placing an apertured reflector, which is part of the measurementdevice, adjacent to the surface;

[0276] illuminating the surface with incident illumination such thatillumination is reflected from portions of the surface and such thatillumination is reflected from or diffracted by the apertured reflector;

[0277] coherently detecting the illumination reflected from the surfaceutilizing the illumination reflected from or diffracted by the aperturedreflector as a local oscillator to form a signal;

[0278] determining the relative motion of the surface perpendicular toand parallel to the apertured reflector from the signal.

[0279] Preferably, coherently detecting comprises:

[0280] detecting amplitude or phase variations of the reflectedillumination; and

[0281] detecting a frequency shift of the reflected illumination; and

[0282] determining the relative motion comprises:

[0283] measuring relative motion of the surface in a direction parallelto the apertured reflector responsive to at least one of the detectedamplitude or phase variations; and

[0284] measuring relative motion of the surface in a directionperpendicular to the surface of the apertured reflector responsive tothe detected frequency shift.

[0285] Preferably, the method includes:

[0286] periodically moving the apertured reflector surface in adirection perpendicular to its surface to add a periodic phase shift tothe illumination reflected therefrom; and

[0287] utilizing said phase shift to measure the motion of the surface.

[0288] There is further provided, in accordance with a preferredembodiment of the invention, a method for determining the relativemotion of a surface with respect to a measurement device comprising:

[0289] illuminating the surface, from a source, with incidentillumination such that illumination is reflected from portions of thesurface toward a detector;

[0290] spatially filtering the reflected illumination such that thephase of the detected optical illumination from a given scatterer on thesurface is substantially constant or linearly related to the translationof the surface;

[0291] generating a signal by the detector responsive to theillumination incident on the detector; and

[0292] determining the relative motion of the surface from the signal.

[0293] Preferably, illuminating comprises illuminating the surface withspatially varying illumination.

[0294] Preferably, illuminating the surface comprises illuminating thesurface through an apertured reflector placed adjacent to the surfacewhich reflects or diffracts illumination to the detector. Preferably,generating a signal comprises coherent detection of the illuminationreflected from the surface utilizing the illumination reflected ordiffracted from the apertured reflector.

[0295] Preferably, determining the relative motion comprises utilizing aDoppler shift of the reflected illumination.

[0296] Preferably, the illumination of the surface is substantiallycollimated; and the spatial filter filters the reflected illuminationsuch that substantially only a single spatial frequency of the reflectedillumination is detected by the detector.

[0297] Preferably, illumination of the surface is substantiallycollimated; and spatial filtering filters the reflected illuminationsuch that only illumination reflected from the surface substantially ina single direction is detected by the detector.

[0298] In a preferred embodiment of the invention, spatial filteringcomprises focusing the reflected illumination with a lens having a focalpoint; and placing a pinhole at the focal point of the lens.

[0299] In a preferred embodiment of the invention, spatial filteringcomprises focusing the reflected illumination with a lens having a focalpoint; and placing a single mode optical fiber at the focal point of thelens to transfer illumination to the detector.

[0300] In a preferred embodiment of the invention, spatial filteringcomprises focusing the reflected illumination with a lens; and placing apinhole at an image of the source.

[0301] In a preferred embodiment of the invention, spatial filteringcomprises focusing the reflected illumination with a lens; and placing asingle mode optical fiber at an image of the source to transferillumination to the detector.

[0302] There is further provided, in accordance with a preferredembodiment of the invention, a method for determining the relativemotion of a surface with respect to a measurement device comprising:

[0303] placing an object, having at least a quasi-continuoustransmission function, adjacent to the surface;

[0304] illuminating the surface with incident illumination such thatillumination is reflected from portions of the surface toward adetector;

[0305] detecting the illumination reflected from the surface utilizingthe detector to generate a signal; and

[0306] determining the relative motion of the surface from the signal.

[0307] Preferably, the object has an asymmetric transmission function;and determining the relative motion comprises determining the directionof motion based on the detected signal.

[0308] Preferably, illumination is reflected from or diffracted by theobject toward the detector; and the detection is coherent detectionutilizing the illumination reflected from or diffracted by the object asa local oscillator to form a signal.

[0309] There is further provided, in accordance with a preferredembodiment of the invention, a method for determining the relativemotion of a surface with respect to a measurement device comprising:

[0310] illuminating the surface with illumination, through an aperturedreflector, such that illumination is reflected from the surface toilluminate a detector with illumination which is not an image of a pointon or a portion of the surface;

[0311] simultaneously illuminating the detector with referenceillumination derived from said incident illumination; and

[0312] coherently detecting the reflected illumination of the detectorutilizing said reference illumination such that the detector generates asignal;

[0313] determining the relative motion of the surface parallel to thesurface, based on variations of the signal caused by the relativemotion.

[0314] Preferably, the incident illumination is at a given wavelengthand the reference illumination is at the same wavelength such that thecoherent detection is homodyne detection.

[0315] Preferably, the method includes spatially varying theillumination of the surface. Preferably, spatially varying theillumination of the surface comprises illuminating the surface through atransmission grating having spatially varying periodic transmission.

[0316] Preferably, spatially varying the illumination of the surfacecomprises illuminating the surface through a grating which specularlyreflects a portion of the illumination incident upon it toward thedetector to form said reference illumination.

[0317] There is further provided, in accordance with a preferredembodiment of the invention, a method for determining the relativemotion of a surface with respect to a measurement device comprising:

[0318] illuminating the surface with illumination such that illuminationis reflected from portions of the surface;

[0319] placing an apertured reflector adjacent to the surface;

[0320] coherently detecting the illumination reflected from the surface,utilizing illumination reflected from or diffracted by the aperturedreflector as a local oscillator; and

[0321] determining the relative motion of the surface, in a directionparallel to the surface, from a characteristic of the signal.

[0322] Preferably, the relative motion is detected utilizing a Dopplershift of the illumination reflected from the surface.

[0323] Preferably, the apertured reflector is a grating and illuminationdiffracted by the grating is used in determining the motion.

[0324] In a preferred embodiment of the invention, the illumination isperpendicularly incident on the surface.

[0325] In a preferred embodiment of the invention, the surface isoptically diffusely reflecting surface.

[0326] In a preferred embodiment of the invention, the surface has nomarkings indicating position.

[0327] Preferably, the illumination comprises visible illumination.Alternatively, or additionally, the illumination comprises infraredillumination.

[0328] There is further provided, in accordance with a preferredembodiment of the invention, apparatus for determining the relativemotion of a surface and the apparatus, comprising:

[0329] a partially transmitting object situated adjacent to the surface;

[0330] a detector that detects illumination incident on it and generatesa detected signal;

[0331] a source of illumination which illuminates the object withincident illumination such that illumination is reflected or diffractedtowards the detector from the object and such that part of the incidentillumination is reflected from of the surface towards the detector, suchthat the detector coherently detects the illumination reflected from thesurface utilizing the illumination reflected or diffracted towards thedetector from the object; and

[0332] circuitry which determines relative motion of the surfaceparallel to the surface with respect to the apparatus from the detectedsignal.

[0333] There is further provided, in accordance with a preferredembodiment of the invention, an optical mouse comprising:

[0334] a housing having an aperture facing a surface; and

[0335] an optical motion detector which views the surface through theaperture, wherein the optical motion detector utilizes the method of theinvention to determine the translation of the housing with respect tothe surface.

[0336] There is further provided, in accordance with a preferredembodiment of the invention, a touch point for use as a control device,comprising:

[0337] a housing having an aperture; and

[0338] an optical detector which determines the motion of a finger whichis translated across the aperture.

[0339] Preferably, the optical detector utilizes the method of theinvention to determine the translation.

[0340] There is further provided, in accordance with a preferredembodiment of the invention, a pointer device comprising:

[0341] a first touch point according to the invention and circuitrywhich moves a pointer responsive thereto; and

[0342] a second touch point according to the invention and includingcircuitry which causes scrolling responsive thereto.

[0343] There is further provided, in accordance with a preferredembodiment of the invention, a combination mouse/touch point for use asa pointer for a computer comprising:

[0344] a housing having an aperture;

[0345] an optical detector which determines the motion of an objectwhich is translated across the aperture; and

[0346] means for determining whether the aperture is upward or downwardfacing.

[0347] Preferably the optical detector utilizes the method of theinvention to determine the translation.

[0348] There is further provided, in accordance with a preferredembodiment of the invention, a scanner for reading a document bymovement of the scanner over the document comprising:

[0349] an optical reading head which detects patterns on the surface ofthe document; and

[0350] an optical detector which determines the motion of the scanner asit is translated across the surface of the document, wherein the opticaldetector utilizes the method of the invention to determine thetranslation.

[0351] Preferably, the patterns comprise printed patterns. Alternativelyor additionally, the patterns comprise handwritten patterns.Alternatively or additionally, the patterns comprise a signature.

[0352] There is further provided, in accordance with a preferredembodiment of the invention, an encoder comprising:

[0353] an optically diffusely reflecting surface; and

[0354] an optical detector having relative motion with respect to thesurface, wherein the optical detector measures relative motion withrespect to the surface without utilizing markings on the surface.

[0355] There is further provided, in accordance with a preferredembodiment of the invention, an encoder comprising:

[0356] an optically diffusely reflecting surface having no markingsother than reference markings; and

[0357] an optical detector having relative motion with respect to thesurface, wherein the optical detector measures relative motion withrespect to the surface relative to the reference markings.

[0358] Preferably, the surface is the surface of a disk which rotatesabout an axis and wherein the detector measures the rotation of thedisk.

[0359] Preferably, the encoder utilizes the method of the invention.

[0360] There is further provided, in accordance with a preferredembodiment of the invention, a virtual pen comprising:

[0361] an encoder according to the invention; and

[0362] circuitry which translates said measured relative motion intowritten or graphical data.

[0363] There is further provided, in accordance with a preferredembodiment of the invention, a device for moving a sheet of papercomprising:

[0364] means for moving the paper; and

[0365] an optical detector which measures the movement of the paperwithout utilizing any markings on the paper.

[0366] Preferably, the optical detector utilizes the method of theinvention.

[0367] There is further provided, in accordance with a preferredembodiment of the invention, a

[0368] a device for moving a sheet according to the invention;

[0369] a reading head which reads information from the paper; and

[0370] a memory which stores the information in memory locationsresponsive to the measurement of movement of the paper.

[0371] There is further provided, in accordance with a preferredembodiment of the invention, a printing machine comprising:

[0372] a device for moving a sheet according to the invention;

[0373] memory which contains information to be printed on the sheet ofpaper; and

[0374] a printing head which prints the information responsive to themeasurement of movement of the paper.

[0375] There is further provided, in accordance with a preferredembodiment of the invention, a facsimile machine comprising a scanneraccording to the invention.

[0376] There is further provided, in accordance with a preferredembodiment of the invention, a facsimile machine comprising a printeraccording to the invention.

[0377] There is further provided, in accordance with a preferredembodiment of the invention, a method for determining the direction ofrelative motion of a surface with respect to a measurement devicecomprising:

[0378] illuminating the surface with incident illumination such thatillumination is reflected from portions of the surface toward adetector;

[0379] placing an object, having an asymmetric transmission function,adjacent to the detector;

[0380] detecting the illumination reflected from the surface utilizingthe detector to generate a signal; and

[0381] determining the direction of relative motion of the surface fromthe signal.

BRIEF DESCRIPTION OF THE DRAWINGS

[0382] The present invention will be more clearly understood from thefollowing description of preferred embodiments of the invention read inconjunction with the attached drawings in which:

[0383]FIG. 1 is a schematic representation of a preferred embodiment ofa motion transducer, in accordance-with a preferred embodiment of theinvention;

[0384]FIG. 2 is a graph of a grating transmission function, inaccordance with a preferred embodiment of the invention;

[0385]FIGS. 3A, 3B and 3C are schematic representations of preferredembodiments of integrated motion transducers, in accordance withpreferred embodiments of the invention;

[0386]FIG. 4 is a schematic diagram of an optical mouse in accordancewith a preferred embodiment of the invention;

[0387]FIGS. 5A and 5B are schematic diagrams of a mouse/fingertranslation measurement device, in accordance with a preferredembodiment of the invention;

[0388]FIG. 6 is a schematic diagram of a scanning pen in accordance witha preferred embodiment of the invention;

[0389]FIG. 7 is a diagram of a rotation encoder, in accordance with apreferred embodiment of the invention;

[0390]FIG. 8 is a schematic diagram of a fiber-optic-based translationmeasurement device, in accordance with a preferred embodiment of theinvention;

[0391]FIG. 9 is a simplified and generalized block diagram of electroniccircuitry, suitable for use in preferred embodiments of the invention;

[0392]FIG. 10 is a simplified diagram of a translation measurementdevice according to an alternative preferred embodiment of theinvention;

[0393]FIGS. 11A and 11B illustrate yet another preferred embodiment ofthe invention;

[0394]FIGS. 12A and 12B illustrate the principle of a first preferredembodiment of the invention utilizing a mechanical switching system todetermine the direction of motion of a translation measurement device,in accordance with a preferred embodiment of the invention;

[0395] FIGS. 13A-13D illustrate the principles of two additionalpreferred embodiments of the invention utilizing a mechanical switchingsystem to determine the direction of motion of a translation measurementdevice;

[0396] FIGS. 14-16 illustrates the principles of three translationmeasurement devices, in accordance with a preferred embodiment of theinvention which do not utilize a grating;

[0397]FIGS. 17 and 18 illustrate the principles of two additional motiondetectors, according to preferred embodiments of the invention, thatmeasure surface motion based on a Doppler shift;

[0398]FIGS. 19A and 19B schematically show integrated structures thatoperate according to the same principles as the apparatus of FIGS. 15and 16, combined with direction detection as in FIGS. 3C, 17 and 18;

[0399]FIGS. 19C and 19D schematically show details of a detector moduleutilized in some preferred embodiments of the invention;

[0400]FIGS. 20A and 20B shows two views of a general structure for adevice for the measurement of rotation of a relatively small shaft, inaccordance with preferred embodiments of the invention;

[0401]FIG. 21 schematically shows a configuration of detectors usefulfor reducing the effects of motion, normal to the surface, onmeasurements of motion parallel to the surface, in accordance with apreferred embodiment of the invention;

[0402] FIGS. 22A-22D schematically illustrate various configurations ofdetectors, in accordance with preferred embodiments of the invention,for determining two dimensional motion along the plane of a surface;

[0403]FIG. 23 illustrates curves of cursor velocity as a function ofsurface velocity for various filtration techniques;

[0404]FIG. 24 illustrates a diffraction grating useful in preferredembodiments of the invention;

[0405]FIG. 25 illustrates a second diffraction grating produced inaccordance with a preferred embodiment of the invention; and

[0406] FIGS. 26A-26C illustrate positioning of source, detector andgrating in which the detectors are positioned far from the specularreflection from the surface, in accordance with a preferred embodimentof the invention; and

[0407]FIG. 27 is a schematic circuit drawing of a preferred embodimentof an adaptive band pass circuit useful for some aspects of theinvention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS OF THE INVENTION

[0408]FIG. 1 shows apparatus 10 for the measurement of the translationof a surface 12, in accordance with a preferred embodiment of theinvention. Apparatus 10 comprises a source of at least partiallycoherent, preferably collimated optical radiation 14, such as a laser.Preferably, the laser is a diode laser, for example a low powerinfra-red laser. While other wavelengths can be used, an infra-red laseris preferred since it results in eye-safe operation at higher power. Thesource is preferably collimated. While it is desirable to use acollimated beam from depth of field considerations, the collimation neednot be particularly good. However, a non-collimated source may be usedif compensation as described below is used.

[0409] Apparatus 10 also includes a one-dimensional or two dimensionalreflective grating 16, which is closely spaced from surface 12. Thelimitations as to spacing of grating 16 from surface 12 are describedbelow. Typically the spacing between grating 16 and surface 12 is a fewmillimeters or less. Light which is reflected from (or diffracted by)grating 16 and light reflected by surface 12 are both preferablyincident on a spatial filter (composed of a lens 18 and a pinhole 20)before being detected by an optical detector 22. The resultinginterference gives rise to a beat signal that depends on the motion ofthe surface. As indicated from FIG. 1, radiation is reflected from thesurface in substantially all directions. This radiation is omitted fromsome of the drawings for clarity of presentation.

[0410] In FIG. 1 the light is seen as being incident on the surface froman angle; however, it is possible for the light to be incident at thenormal to grating 16. Moreover, while FIG. 1 shows the incident lightangle equal to the detection angle, such that light reflected from thegrating (or zeroth order diffraction) is used for the local oscillator,first or higher order diffraction by the grating can be effectivelyused. Zero order has the advantages that it is wavelength independent(stability of the wavelength is not important). The incident light canbe pulsed or continuous. In FIG. 1, light diffracted at the −1 and +1orders are indicated by reference numbers 19 and 21 respectively. Lightthat is scattered by the surface is indicated by reference number 17.

[0411] In the preferred embodiment of the invention shown in FIG. 1,speckle-free, coherent detection (homodyne or heterodyne, homodyne shownin FIG. 1) is used to determine tangential motion. Such detectionresults in an intrinsic amplification of the signal used for measurementresulting in a high dynamic range.

[0412] The reference local oscillator field for the coherent detectionis provided by reflections from grating 16, placed close to the movingsurface. The interference of the reflections from the grating and themoving surface on the detector give rise to a translation dependentoscillating signal. The incorporation of a near-surface reflection froma grating as the origin of the local oscillator field may give multipleadvantages, including at least some of the following:

[0413] 1. The grating is a single element that combines the roles of abeam splitter and a mirror in a coherent homodyne/heterodyne detectionoptical setup, thus making the optical system simple, robust and withfew alignment requirements.

[0414] 2. The grating causes spatially periodic intensity and/or phasemodulation of the illumination reflected from the surface, if thesurface is placed within the near field of the grating. This enablesdetection of translation using the specular (zeroth order) reflection asthe reference wave.

[0415] 3. High order diffractions (±1^(st), ±2^(nd), etc.) from thegrating serve as local oscillator fields for detection of the surface'stranslation utilizing the Doppler shift of the surface reflection. Atranslation dependent phase shift between the reference and surfacewaves at non-specular reflection orders produce oscillationsrepresentative of the translation. The resolution increases for higherdiffraction orders.

[0416] 4. Translation detection can be frequency biased by periodicshifting of the grating position (e.g. sawtooth modulation), enablingdetermination of direction as well as magnitude of the translation.

[0417] 5. A two-dimensional grating provides reference (localoscillator) waves and modulation of the illumination of the surface andreflections from it for two orthogonal translation directions in asingle element, for two-dimensional transverse motion measurement.

[0418] 6. Measurement at different grating orders provides differentcomponents of the translation or velocity vector of the surface. Forspecular reflection, for example, translation along the axisperpendicular to the grating can be measured independently oftranslation in the other directions. This allows for three dimensionaltranslation measurement.

[0419] 7. Asymmetric grating transmission functions (amplitude and/orphase) enable direction detection in all reflected orders, usingappropriate signal manipulation/analysis.

[0420] 8. Frequency biasing using local oscillator phase shifting, incombination with the amplitude modulation resulting from the grating atnear field provide for simultaneous measurement of 2-D translation (in atransverse and axial translation plane) using a single detector.

[0421] In addition to spatial filtering related restrictions, theallowed distance between the grating and the surface generally dependson the grating period Λ, the light wavelength λ, the spectral coherencewidth Δλ, the illuminated area and the incident and reflected beamangles.

[0422] For those preferred embodiments of the invention, which utilizethe light reflected or diffracted from the grating as a localoscillator, it is most preferable for the spacing between the surface 12and the grating 16 to be smaller than the coherence length of the light,given by ≈λ²/Δλ, where Δλ is the spectral width of radiation reachingthe detector (and not necessarily the spectral width of the lightsource). Furthermore, the coherence length of the source shouldpreferably be larger than nλL/Λ, to maintain the coherence across thediffracted beam width, where L is the width of the illuminating beam. Byproper spectral filtering along the optical path, the spectral contentreaching the detector can be limited and its coherence length increased,if this is necessary.

[0423] For those preferred embodiments of the invention, in which themodulated transmission pattern plays a major role in the detectionscheme, the spacing between the grating and surface 12 should also bewithin the near-field distance from the grating, ≈Λ²/4λ. For thefollowing embodiments the spacing is assumed to be near field. Thisrequirement is relaxed for the cases where it is not essential.

[0424] Relative motion of the surface can be measured in a number ofways. Consider the incident field and the grating field transmissionfunction, respectively:

E(t)=E ₀ cos(ω₀ t)   (1)

A(x)=Σ_(m) c _(m) cos(2πmx/Λ+ψ _(m))   (2)

[0425] The grating is assumed to be a pure amplitude grating with periodΛ, so that its transmission is the sum over non-negative spatialfrequencies with real coefficients. A similar formalism applies also tobinary phase grating, or some general phase gratings, which can also beused in the practice of the present invention. For the general case ofboth amplitude and phase gratings a phase retardation term is added. Forsimplicity of the description the following description is based on apure amplitude grating. However, it should be understood that othergratings can be utilized and are preferable for some embodiments of theinvention. Unimportant constant factors are also omitted in variousparts of the following mathematical treatment.

[0426] Plane-wave illumination by the light source over the grating areais assumed (i.e.—a collimated beam), but is not strictly necessaryprovided, for example, the non-collimation is compensated in anotherpart of the system (e.g.—the spatial filter). It is assumed forsimplicity that the incident light is perpendicular to the grating (andnot as shown in FIG. 1). Oblique incident light (in the direction of thegrating lines and/or perpendicular to it) gives substantially the sameresults, with shifted reflection angles. Thus, the grating fieldcontains a series of reflected diffraction orders, arrangedsymmetrically about the specular reflection component (zeroth order) andobeying the angular condition (for the n-th order):

sin(α)=nλ/Λ.   (3)

[0427] As shown in FIG. 1, a spatial filter in front of the detector ispreferably comprised of focusing lens 18 and narrow pinhole 20 at thefocal point of the lens. Such a spatial filter is preferably adjusted toselect only a single spatial frequency component to reach the detector.The pinhole can be replaced by a single-mode optical fiber, having asimilar core diameter and leading the light to a remote detector. Thespatial filter is aligned such that one of the diffraction ordersreaches the detector, and serves as the local oscillator for homodynedetection of the reflected radiation, or for heterodyne detection asdescribed below. The local oscillator field is given by:

E _(LO)(t)=E _(n) cos(ω₀ t+φ _(n))   (4)

[0428] The reflected field from the moving surface in the same directionas the n-th diffraction order is represented by an integral over theilluminated surface area of independent reflections from the surface.Integrating over the direction parallel to the grating lines (y) andover the direction normal to the surface (corresponding to lightpenetration into the surface), results in a reflected field equal to:$\begin{matrix}\begin{matrix}{{E_{r}(t)} = {E_{0}{\int_{x_{1}}^{x_{2}}{{{{xA}(x)}}{r\left( {x - {p(t)}} \right)}{\cos\left( {{\omega_{0}t} +} \right.}}}}} \\{\left. {{2\quad \pi \quad {{nx}/\Lambda}} + {\varphi \left( {x - {p(t)}} \right)}} \right)}\end{matrix} & (5)\end{matrix}$

[0429] where r(x) and φ(x) are location dependent amplitude and phasereflectance of the surface, respectively. The reflectance is assumed tobe time-independent during the measurement, with both r and φ beingrandom variables of the position x. The translation of the surface fromits initial position is given by p(t), with p(0)=0. The periodic phaseterm 2πnx/Λ arises from the reflection at an angle sin(α)=nλ/Λ. Theintegration limits are from x₁ to x₂, both determined by the illuminatedarea.

[0430] Changing the integration variable from x to x-p(t), correspondingto the symmetric situation of a static surface and moving grating withrespect to the reference coordinate system: $\begin{matrix}\begin{matrix}{{E_{r}(t)} = {E_{0}{\int_{x_{1} - {p{(t)}}}^{x_{2} - {p{(t)}}}{{{{xA}\left( {x + {p(t)}} \right)}}{r(x)}{\cos\left( {{w_{0}t} + {2\quad \pi \quad {{{np}(t)}/L}} +} \right.}}}}} \\{\left. {{2\quad \pi \quad {{nx}/L}} + {f(x)}} \right)}\end{matrix} & (6)\end{matrix}$

[0431] with integration limits now extending from x₁-p(t) to x₂-p(t) andthus being time-dependent. Replacing A(x) with its Fourier series andwriting φ_(n)(x)=φ(x)+2πnx/Λ gives: $\begin{matrix}\begin{matrix}{{E_{r}(t)} = {E_{0}{\int_{x_{1} - {p{(t)}}}^{x_{2} - {p{(t)}}}{{x}{\sum\limits_{m}{c_{m}{\cos\left( {{2\pi \quad m\quad {x/\Lambda}} + {2\quad \pi \quad m\quad {{p(t)}/\quad \Lambda}} +} \right.}}}}}}} \\{{\left. \psi_{m} \right){r(x)}{\cos \left( {{\omega_{0}t} + {2\quad \pi \quad n\quad {{p(t)}/\Lambda}} + {\varphi_{n}(x)}} \right)}}}\end{matrix} & (7)\end{matrix}$

[0432] The (optical) phase of a scatterer on the surface linearlydepends on the translation p(t), with φ=φ_(n)(x)+2πnp(t)/Λ. For specularreflection (n=0), the phase is a constant. Both the reflected field andthe local oscillator field reach the detector. Since the detectormeasures intensity, which is proportional to the square of the field,the intensity is given by:

I(t)=(E _(LO)(t)+E _(r)(t))² =E _(LO)(t)²+2E _(LO)(t) E _(r)(t)+E_(r)(t)²   (8)

[0433] Assume that the local oscillator field is much larger than thereflected field, E_(LO)>>E_(r) and that the detector integration time ismuch longer than an optical period time but much shorter than Λ/nV_(max)(where V_(max) is the maximum measured velocity). Integration overoptical frequencies gives just a DC component while other variations aredetected instantaneously. Under these assumptions, the first intensityterm is replaced by a constant I_(LO)=0.5E_(LO) ² and the thirdintensity term is neglected, i.e., I_(r)=0.5E_(r) ²=0. In this preferredembodiment of the invention, the ratio of the strength of the localoscillator field and of the reflected field is intrinsically large,since the reflection from the grating is directed only to specificnarrow orders and the reflection from the diffuse surface is scatteredover a broad angle.

[0434] While the following discussion assumes that the third term iszero, translation measurement utilizing the spatial transmissionmodulation is possible even if the third term alone is present, i.e.,when the light reflected from the surface is not combined with areference reflected or diffracted from the grating. This may be achieved(if desired) by selecting an angle that lies between grating orders. Itdoes have the advantage of significantly relaxed alignment constrains(it only requires that the light be in the focal plane of the spatialfilter), but will generally be less accurate and with a lowsignal-to-noise ratio.

[0435] The local oscillator field serves as a very strong amplifier inthe first stage of signal detection. In this respect it is stronglypreferred to keep the local oscillator field as noise-free as possible,since its noise transfers to the detected signal directly.

[0436] The measured cross term is equal to:

I _(s)(t)=E _(n) cos(ω₀ t+φ _(n))E _(r)(t)   (9)

[0437] Inserting the oscillating field term cos(ω₀t) into the integralfor E_(r)(t) and using the cosine sum relationship cos α cosβ=0.5(cos(α+β)+cos(α−β)) for the right-most cosine in (7), results inone intensity component at twice the optical frequency (2ω₀) and anotherwith slowly varying phase. The fast oscillating component averages tozero because of the detector's time response. The remaining signal is:$\begin{matrix}\begin{matrix}{{I_{S}(t)} = {I_{n}{\int_{x_{1} - {p{(t)}}}^{x_{2} - {p{(t)}}}{{x}{\sum\limits_{m}{c_{m}{\cos\left( {{2\pi \quad {{mx}/\Lambda}} + {2\pi \quad m\quad {{p(t)}/\Lambda}} +} \right.}}}}}}} \\{{\left. \psi_{m} \right){r(x)}{\cos \left( {{2\quad \pi \quad n\quad {{p(t)}/\Lambda}} + {\varphi_{n}(x)} - \phi_{n}} \right)}}}\end{matrix} & (10)\end{matrix}$

[0438] Exchanging summation with integration, the contribution of eachterm to the sum is: $\begin{matrix}\begin{matrix}{{I_{s,m}(t)} = {I_{n}c_{m}{\int_{x_{1} - {p{(t)}}}^{x_{2} - {p{(t)}}}{{x}\quad {\cos\left( {{2\pi \quad {{mx}/\Lambda}} + {2\pi \quad m\quad {{p(t)}/\Lambda}} +} \right.}}}}} \\{{\left. \psi_{m} \right){r(x)}{\cos \left( {{2\quad \pi \quad {{{np}(t)}/\Lambda}} + {\varphi_{n}(x)} - \phi_{n}} \right)}}}\end{matrix} & (11)\end{matrix}$

[0439] Assume that c₀, c₁>>{c_(m), m>1}. This last requirement enablesus to concentrate on just two terms in the sum over grating harmonics,the m=0 and m=1 terms. For these two terms we can write: $\begin{matrix}{{I_{s,0}(t)} = {I_{n}c_{0}{\int_{x_{1} - {p{(t)}}}^{x_{2} - {p{(t)}}}{{{{xr}(x)}}{\cos \left( {{2\quad \pi \quad n\quad {{p(t)}/\Lambda}} + {\varphi_{n}(x)} - \phi_{n}} \right)}}}}} & (12) \\{{{I_{s}}_{,1}(t)} = {I_{n}c_{1}{\int_{x_{2} - {p{(t)}}}^{x_{2} - {p{(t)}}}{{x}\quad {\cos \left( {{2\pi \quad {x/\Lambda}} + {2\pi \quad {{p(t)}/\Lambda}} + \psi_{1}} \right)}{r(x)}{\cos \left( {{2\quad \pi \quad {{{np}(t)}/\Lambda}} + {\varphi_{n}(x)} - \phi_{n}} \right)}}}}} & (13)\end{matrix}$

[0440] Attention is now focused on specific diffraction orders in thereflected and diffracted waves from the grating, the n=0 (specularreflection) and n=±1 directions.

[0441] For the specular reflection term, the m=0 contribution is:$\begin{matrix}{{I_{s,0}(t)} = {I_{0}c_{0}{\int_{x_{1} - {p{(t)}}}^{x_{2} - {p{(t)}}}{{x}\quad {r(x)}\cos \quad \left( {\varphi (x)} \right)}}}} & (14)\end{matrix}$

[0442] For a diffuse surface with constant brightness this term will benearly constant, and will change slowly as and when the averagereflection from the surface changes. The m=1 term is: $\begin{matrix}\begin{matrix}{{I_{s,1}(t)} = {I_{0}c_{1}{\int_{x_{1} - {p{(t)}}}^{x_{2} - {p{(t)}}}{{x}\quad {\cos\left( {{2\quad \pi \quad {x/\Lambda}} + {2\pi \quad {{p(t)}/\Lambda}} +} \right.}}}}} \\{{\psi_{1}{r(x)}{\cos \left( {\varphi (x)} \right)}} =} \\{{{\cos \left( {2\quad \pi \quad {{p(t)}/\Lambda}} \right)}I_{0}c_{1}{\int_{x_{1} - {p{(t)}}}^{x_{2} - {p{(t)}}}{{x}\quad {\cos \left( {{2\quad \pi \quad {x/\Lambda}} + \psi_{1}} \right)}{r(x)}{\cos \left( {\varphi (x)} \right)}}}} -} \\{{{\sin \left( {2\quad \pi \quad {{p(t)}/\Lambda}} \right)}I_{0}c_{1}{\int_{x_{1} - {p{(t)}}}^{x_{2} - {p{(t)}}}{{x}\quad {\sin \left( {{2\quad \pi \quad {x/\Lambda}} + \psi_{1}} \right)}{r(x)}{\cos \left( {\varphi (x)} \right)}}}} \equiv} \\{{{{\cos \left( {2\quad \pi \quad {{p(t)}/\Lambda}} \right)}{I_{c}(t)}} + {{\sin \left( {2\quad \pi \quad {{p(t)}/\Lambda}} \right)}{I_{s}(t)}}} \equiv} \\{{I(t)}{\cos \left( {{2\quad \pi \quad {{p(t)}/\Lambda}} + {\vartheta (t)}} \right)}}\end{matrix} & (15)\end{matrix}$

cos(2πp(t)/Λ)I _(c)(t)+sin(2πp(t)/Λ)I _(s)(t)≡I(t)cos (2πp(t)/Λ+θ(t))

[0443] where the intensity I(t) and phase θ(t) result from integralsover random variables corresponding to the amplitude and phasereflection of the diffuse surface at a spatial frequency 1/Λ. Fordiffuse surfaces with single reflectors larger than the spatialwavelength Λ the contribution will come from grain boundaries, while fordiffuse surfaces having small particle sizes there will be strongcontributions for all spatial frequencies up to 1/d, where d is theaverage particle size.

[0444] The rate of change of these “random walk” variables depends onthe average time it takes a given set of reflection centers {x_(i)} tobe replaced by a new set, which in turn is related to the change of theintegration region above, τ∝(x₁-x₂)/v=L/v, where v is the instantaneousvelocity and L is the illuminated size of the grating. If a large numberof grating periods are illuminated such that L>>Λ, the result is fastoscillations with a slowly varying statistical amplitude and phase. Theerror of the translation measurement is proportional to Λ/L and isindependent of the velocity.

[0445] In summary, for specular reflection translation measurement:

[0446] 1. The measured signal at the detector output oscillates at afrequency of v/Λ. Detection and counting of the zero crossing points ofthis signal gives a direct translation measurement, each zero crossingcorresponding to a Δp=Λ/2 translation, provided that the translationdirection does not change during the measurement.

[0447] 2. The measured signal's amplitude and phase are slowly varyingstatistical ensemble sums. The relative accuracy of the measurement isproportional to Λ/L, L being the illuminated grating size.

[0448] 3. The spacing between the surface and the grating shouldpreferably be smaller than both the near field distance, ≈Λ²/4λ, and thecoherence length of the light reaching the detector, ≈λ²/Δλ.

[0449] The first order reflection, unlike the specular reflection,carries also a Doppler phase shift. Looking again at the contribution ofthe m=0,1 spatial frequency components gives: $\begin{matrix}{{I_{s,0}(t)} = {I_{1}c_{0}{\int_{x_{1} - {p{(t)}}}^{x_{2} - {p{(t)}}}{{{{xr}(x)}}{\cos \left( {{2\quad \pi \quad {{p(t)}/\Lambda}} - {\varphi_{1}(x)} - \phi_{1}} \right)}}}}} & (16) \\{{{I_{s}}_{,1}(t)} = {I_{1}c_{1}{\int_{x_{1} - {p{(t)}}}^{x_{2} - {p{(t)}}}{{x}\quad {\cos \left( {{2\pi \quad {x/\Lambda}} + {2\quad \pi \quad p\quad {(t)/\Lambda}} + \psi_{1}} \right)}{r(x)}{\cos \left( {{2\quad \pi \quad {{p(t)}/\Lambda}} + {\varphi_{1}(x)} - \phi_{1}} \right)}}}}} & (17)\end{matrix}$

[0450] Using a decomposition of the cosine term in (16) as in (15)results in:

I _(s,0)(t)=I ₀(t)cos(2πp(t)/Λ+θ₀(t))   (18)

[0451] In a similar manner the expression for the m=1 term, (17) is:

I _(s,1)(t)=I ₁(t)cos(4πp(t)/Λ+θ₁(t))   (19)

[0452] Equation (19) neglects a slowly varying term that adds to theaverage detector signal (the “DC” component). An analysis of equations(16)-(19) shows that if c₀>>c₁, the zero crossings of the signalcorrespond to Δp=Λ/2, while if c₀<<c₁, zero crossings correspond toΔp=Λ/4. This result can be expanded to other reflection orders n>1,where, if c₀>>c₁ the measured signal will oscillate according tonp(t)/Λ. For |n|>1, the c₁ term amount to oscillations in two side bandsaround the c₀ oscillations as in amplitude modulation of a higherfrequency signal. Notice that the m=0 term does not require near fieldconditions, so by fixing the distance to the moving surface so it islarger than the near field limit ≈Λ²/4λ (but preferably smaller than thecoherence length ≈λ²/Δλ), the m=0 contribution is dominant.Alternatively, a transmission function for the grating such that c₀>>c₁even in the near field is preferably used.

[0453] In a preferred Doppler mode of operation, a grating is utilizedfor the generation of a local oscillator field by diffracting incidentillumination towards the detectors. However, diffraction orders mayexist in transmission as well (e.g., when a pure amplitude grating isused). These orders may result in multiple-beam illumination of thesurface even outside of the near field of the grating and in diffractionof the illumination reflected from the surface toward the detector intomultiple beams. Thus, each detector will detect a multitude of Dopplercomponents, each corresponding to the Doppler shift of a combination oftransmitted and reflected orders interfering with the local oscillatorfield illuminating the detector, constituting ‘optical cross-talk’.

[0454] In a preferred embodiment of the invention, illumination of thesurface is by a single beam, eliminating the above mentioned ‘opticalcross talk’. Similarly, it is desirable that the reflected illuminationfrom the surface should not be diffracted by the grating. Thus, thenon-zero transmission orders of the grating should be minimized andpreferably eliminated. A diffraction grating is preferably used for thegeneration of the local oscillator fields using orders in reflection,and designed to have virtually only a single transmission order (i.e., asingle beam illuminating the surface and the illumination of the surfacedoes not constitute an interference pattern on the surface). Also, theillumination reflected from the surface is not forward diffracted whenpassing through the grating toward the detectors, as desired.

[0455] Reference is made to FIG. 24 which illustrates an exemplarydiffraction grating 800 which embodies this principle. Assume thegrating is a binary phase grating with refractive index of n_(g),suspended in a medium of another refractive index n_(s). The gratingpreferably embodies square grooves 802 of depth h. For incident normalillumination 804, the relative phase difference in reflection from theinner side 806 of the grating is P_(r)=2n_(g)·h/λ, whereas for atransmitted beam 808 the relative phase difference isP_(t)=(n_(g)−n_(s))·h/λ. Negligible high-orders in transmission will beobtained when P_(t) is a natural number, so that the minimum groovedepth is h=λ/(n_(g)−n_(s)). At the same time, the reflection efficiencydepends on the optical phase difference in reflection, which aftersubstitution of the groove depth is:$P_{r} = {\frac{2\quad n_{g}}{n_{g} - n_{s}}.}$

[0456] If air is assumed on the transmitting side of one grating(n_(s)=1) and minimizing the zero-order reflection (P_(r)=M+½, Mnatural), then: $n_{g} = {\frac{M + \frac{1}{2}}{M - {1\frac{1}{2}}}.}$

[0457] For example, with M=5, wavelength of 850 nm and a refractiveindex n_(g)≅1.57, groove depth of approximately 1.5 micrometer willresult in optimal back diffraction efficiency with ideally only zeroorder transmission.

[0458]FIG. 25 illustrates another method of producing a grating 810having substantially only zero order transmission and having at leastfirst order back diffraction. According to a preferred embodiment of theinvention, a diffractive phase grating 812 is coated by a metallic (ordielectric) layer 814 functioning as a partial reflector with controlledreflection coefficient. This coating can be made e.g., by sputtering orevaporation of the coating material on the grating surface. The otherside of layer 814 is filled by an optical medium 816 with an index ofrefraction essentially equal to that of the grating material.Conveniently, this material may be an optical glue attaching the gratingto a polarizer, a waveplate or a protective glass, indicated byreference 818, or an epoxy mold combining elements 816 and 818.

[0459] In this construction, any optical path difference generated bythe grating on the transmitted radiation is compensated by acorresponding optical path difference in the optical glue, such that thephase front at the exit of the compound arrangement is unaltered. Thus,there are substantially no transmission orders other than the zeroorder. Back diffraction, on the other hand is achieved by the differencein phase of the reflections from layer 814 at different locations, e.g.,the inner edge 820 of grooves 802 and the outer edge 822 of the grooves.

[0460] An advantage of the method illustrated in FIG. 25 is convenientcontrol of the reflected (and back diffracted) and transmitted power ofthe grating illumination, by altering the reflection and transmission oflayer 814. This effect may be utilized, for example, to maximize thesignal to noise and to limit the emission to an eye-safe level.

[0461] The method of eliminating the diffraction of a grating intransmission as illustrated in FIG. 25, is appropriate for complex phasepatterns, and not only binary phase gratings. It is also applicable todiffractive lenses and other diffractive optical elements for whichindependent control of the transmission and the reflection is desired.The transmission may also be modified by a second diffractive orrefractive feature on the other outer surface 824 of the opticalelement.

[0462] The frequency associated with the c₀ oscillations depends on thetransverse as well as axial (perpendicular) translation component(described below). Conversely, the amplitude modulation (through the c₁component) depends solely on the transverse component. When thefrequency of the c₀ oscillations is sufficiently high, this frequencycan be measured by the frequency-related technique described above,simultaneously with the detection of the amplitude modulation frequencyto measure the transverse translation component. In this way, 2-Dtranslation measurement (including motion perpendicular to the plane ofthe surface—i.e., axial translation) may be achieved using a singledetector.

[0463] By frequency biasing the reference signal, the ratio between thecarrier frequency and the amplitude modulation frequency can be madelarge, improving the measurement accuracy as well as allowing fordetection of the direction of translation. Also, using specularreflection from the grating as a local oscillator enables a cleardistinction to be made between the transverse translation component(indicated by the amplitude modulation) and the axial translationcomponent (indicated by the phase or frequency shift of the carrierfrequency).

[0464] Furthermore, the phase shifting may be combined with anasymmetric transmission pattern of the grating (e.g.—sawtooth pattern)for the purpose of transverse translation direction detection.Alternatively, the grating may be displaced for direction detection inthe two dimensions, or a static phase change is used as explained ingreater detail below.

[0465] In essence, for the non-specular diffraction embodiments of theinvention, two quasi-plane waves are selected for detection by thedetector. One of these waves is the result of the nth order diffractionfrom the grating. The second plane wave is generated by the selection ofone plane wave (by the spatial filter) from the reflections from thesurface.

[0466] In summary for translation measurement using non-speculardiffraction (and assuming constant velocity for clarity of thediscussion):

[0467] 1. The measured signal at the detector output oscillates at afrequency of nv/Λ, where n is the order number. Detection and countingof the zero crossing points of this signal gives a direct translationmeasurement, each zero crossing corresponding to Λ/2n translationprovided that the translation direction is not switched during themeasurement.

[0468] 2. The measured signal's amplitude and phase are slowly varyingstatistical ensemble sums. The relative accuracy of the measurement isproportional to Λ/nL, L being the illuminated grating size, which inturn is preferably larger than nλL/Λ.

[0469] 3. The distance between the surface and the grating shouldpreferably be smaller than the coherence length of the light reachingthe detector, λ²/Δλ.

[0470] Even though the absolute time-varying translation |p(t)| can bemeasured very accurately its direction is preferably determined usingone of the methods described below.

[0471] In one preferred embodiment of the invention, direction may bedetermined by applying an additional phase shift between the reference(local oscillator) field and the reflected field. This additional phaseshift can be manifested, for example, by moving the grating towards oraway from the surface. This movement does not change the phase of thefield incident upon the surface, so that the field reflected from thesurface is identical to that given above. The local oscillator field,however, acquires an additional phase shift due to this translation thatdepends on the grating displacement d(t).

[0472] Keeping the distance between the grating and the surface almostconstant and introducing a fixed frequency shift between the reflectedand local oscillator fields can be achieved by making d(t) a periodicsaw-tooth function: $\begin{matrix}\begin{matrix}{{d_{n}(t)} = {D_{n}{\int_{0}^{t}{\left\lbrack {\tau^{- 1} - {\sum\limits_{k = 0}^{\infty}{\delta \left( {t^{\prime} - {k\quad \tau}} \right)}}} \right\rbrack {t^{\prime}}}}}} \\{D_{n} = \frac{\lambda}{1 + \sqrt{1 - \left( \frac{n\quad \lambda}{\Lambda} \right)^{2}}}}\end{matrix} & (20)\end{matrix}$

[0473] with τ as the cycle time for the saw-tooth, fixing the amplitudeof the saw-tooth to give 2π phase shift (or multiples of 2π) forreflection at the nth diffraction order. The frequency shift due to thismotion is τ⁻¹, and if τ⁻¹>nv/Λ is maintained, the direction of themotion is determined without ambiguity according to the frequency ofoscillation of the detector signal, namely τ⁻¹+nv/Λ. Alternatively, thetranslation (both positive and negative) is determined directly bycounting the zero crossing in the detected signal and subtracting itfrom the result of a simultaneous count of the oscillator frequency τ⁻¹.

[0474] If the saw tooth amplitude is not ideal, (i.e., it does notcorrespond to integer multiples of the wavelength) the direction canstill be determined, however, the formulation is more complicated. Asused herein, the term “saw-tooth” includes such non-ideal variations.

[0475] An alternative way of introducing a periodic phase shift betweenthe local oscillator field and the field reflected from the surface isto modulate the optical path length between the grating and the surface.This is preferably achieved by a transparent piezo-electric elementmounted between the grating and the surface.

[0476] An alternative methodology to break the symmetry between positiveand negative relative translation, so that the translation direction canbe detected, is to use an asymmetric function for the transmission(amplitude and/or phase) function of the grating. For simplicity, theformalism is developed for an amplitude grating. For simplicity, assumethat the grating is large compared to the line spacing along thetranslation axis and that k point scatterers are illuminated through thegrating. Scatterers entering or leaving the illuminated area areneglected (this will appear as a noise factor in a comprehensivetreatment). After the interference with the local oscillator (which isnot shifted here) and filtering the optical frequencies, the resultingsignal can be written as: $\begin{matrix}{{I_{s}(t)} = {I_{n}{\sum\limits_{i = 1}^{k}{r_{i}{A\left( {x_{i} + {p(t)}} \right)}{\cos \left( {{2\quad \pi \quad {{{np}(t)}/\Lambda}} + \varphi_{i}} \right)}}}}} & (21)\end{matrix}$

[0477] where r_(i), x_(i) and φ_(i) are the reflectance, the position(at time t=0) and the relative phase (with respect to the localoscillator), respectively, of a scatterer i. For a diffuse body theseare all random variables. This presentation of the detector signal isused for the following direction-detection mechanisms.

[0478] For specular reflection: $\begin{matrix}{{I_{s}(t)} = {I_{0}{\sum\limits_{i = 1}^{k}{r_{i}{A\left( {x_{i} + {p(t)}} \right)}{\cos \left( \varphi_{i} \right)}}}}} & (22)\end{matrix}$

[0479] Assuming that p(t)=vt. i.e.—changes in the surface velocity arerelatively small during the integration time used for determination ofthe translation direction. Thus, the first and second derivatives of thereceived signal are: $\begin{matrix}{{I_{s}^{\prime}(t)} = {I_{0}v{\sum\limits_{i = 1}^{k}{r_{i}{\cos \left( \varphi_{i} \right)}\frac{}{x}\left( {A\left( {x_{i} + {vt}} \right)} \right)}}}} & (23) \\{{I_{s}^{\prime\prime}(t)} = {I_{0}v^{2}{\sum\limits_{i = 1}^{k}{r_{i}{\cos \left( \varphi_{i} \right)}\frac{^{2}}{x^{2}}\left( {A\left( {x_{i} + {vt}} \right)} \right)}}}} & (24)\end{matrix}$

[0480] Assume that A(x) is constructed such that$\frac{^{2}{A(x)}}{x^{2}} = {\eta {\frac{{A(x)}}{x}.}}$

[0481] In this special case it is evident that: I_(s)″(t)=ηv·I_(s)′(t).Thus, the magnitude, and more importantly, the sign of the translationvelocity (i.e.—the translation direction) can be derived from the ratiobetween the first and second time-derivatives of the detector signal.

[0482] If the velocity cannot be assumed to be constant during thedirection-decision integration time, then the derivatives may beperformed with respect to the measured translation (which is known fromthe zero-crossing or from another detector with higher accuracy operatedin parallel). If only the direction is required (and not the velocitymagnitude), it is sufficient to check if the first and secondderivatives carry the same sign (one direction) or not (oppositedirection). A simple XOR (exclusive OR) operation after sign-detectionof the derivatives will be “1” if the sign of η is opposite to the signof v and “0” if they are the same.

[0483] An example of A(x) that satisfies the constant derivative ratiois a combination of exponents like: $\begin{matrix}{{A(x)} = \left\{ \begin{matrix}{{{A\left( {1 - ^{{- {\gamma {({x - {j\quad \Lambda}})}}}/\Lambda}} \right)}:}\quad} & {{{i\quad f\quad j\quad \Lambda} \leq x < {\Lambda \left( {J + \frac{1}{2}} \right)}}\quad} \\{{A\left( {^{{- {\gamma {({x - {{({j + \frac{1}{2}})}\Lambda}})}}}/\Lambda} - ^{- \frac{\gamma}{2}}} \right)}:} & {\quad {{i\quad f\quad {\Lambda \left( {j + \frac{1}{2}} \right)}} \leq x < {\Lambda \left( {j + 1} \right)}}}\end{matrix} \right.} & (25)\end{matrix}$

[0484] where the pattern is repetitive with a cycle Λ. It is evidentthat for this pattern the first and second (and in fact all) derivativeshave a constant ratio as required, of η=−γ/Λ. But, the singularitypoints in multiples of Λ/2 introduce “noise” to the measurement. Thesesingularities increase the error probability as the number of scatterersgrow, since each one will appear in the received signal when a scattererpasses across it. The relative noise contribution is reduced as thedirection detection integration time increases.

[0485] The pattern is assumed to be the intensity of illumination on thesurface. Thus, the requirement for the near field is more stringent thanthe similar requirement for measuring translation magnitude alone in n=0specular reflection. An assumed transmission pattern is shown in FIG. 2,for γ=5. This can be achieved by having a partiallyreflecting/transmitting property for the grating, having an amplitudetransmission function such as that shown in FIG. 2.

[0486] A relaxed requirement from the transmission pattern is that thederivatives will have a constant sign relationship (i.e.—they are notexactly proportional, but their ratio's sign is constant along thepattern). Here, direction-detection is still assured for a singlescatterer, but the error probability is higher than in the former caseas the number of scatterers gets larger (even without the effect of thesingularities).

[0487] A similar analysis is possible for high-order diffraction(|n|>>1). Again, for simplicity the surface is assumed to move with aconstant velocity, v. Equation (21) can be looked at as a sum ofamplitude-modulated signals of a carrier with frequency nv/Λ.

[0488] A(x) is now assumed to be asymmetric (e.g.—sawtooth waveform).For |n|>>1, the detector's signal envelope matches the transmissionfunction for translation in the “positive” direction and is the inverseimage the other way. Thus, if the number of scatterers is small (thelimit being dependent on the grating order n), the translation directionis represented by the sign of the first derivative of the detectedsignal's envelope. In addition, the magnitude of the envelope derivativeis proportional to the magnitude of the translation velocity.

[0489] An asymmetric transmission pattern enables direction detectionfor speckle velocimetry. The detector signal resulting from a randomspeckle pattern, filtered by a grating with intensity transmissionpattern A(x) adjacent to the detector, can be represented as:$\begin{matrix}{{I_{s}(t)} = {I_{0}{\sum\limits_{i = 1}^{k}{r_{i}{A\left( {x_{i} + {p(t)}} \right)}}}}} & (26)\end{matrix}$

[0490] where r_(i) and x_(i) are the intensity and position of the i-th“speckle”, respectively, and p(t) the surface translation. Assumingconstant velocity, p(t)=vt, the detector signal time derivative is:$\begin{matrix}{{I_{s}^{\prime}(t)} = {I_{0}v{\sum\limits_{i = 1}^{k}{r_{i}\frac{}{x}\left( {A\left( {x_{i} + {vt}} \right)} \right)}}}} & (27)\end{matrix}$

[0491] The intensities r_(i) are positive values. Thus, if dA/dx isconstant, then the derivative of the detector signal is indicative ofthe translation direction. Such a pattern is accomplished using sawtoothtransmission pattern. The discontinuities in the pattern add noise tothe measurement, requiring the use of an appropriate integrationinterval in order to limit the error probability. The motion velocity isdetermined from the frequency of oscillations of the detector signal.

[0492] Of course, it is possible to utilize mechanical or other means(e.g.—an accelerometer) to determine the direction of motion as acomplementary component in an OTM device.

[0493] As was noted above, fluctuations in the source amplitude aredirectly transferred to the received signal via the local oscillatorfield. In order to minimize such noise, in accordance with a preferredembodiment of the invention, a signal proportional to the sourceamplitude is detected and the resulting signal (termed the“compensation” detector and signal) is subtracted from the detectorsignal. This detection can be performed, for example, by:

[0494] Splitting the source beam with a beamsplitter (which need not beaccurately aligned) and directing the diverted beam to the compensationdetector, or

[0495] Directing any of the light beams diffracted from the grating to acompensation detector without spatial-filtering it (but potentially withconsiderable attenuation). Conveniently this may be one of the gratingorders not used for the spatial filter measurement. e.g.—use order 1 forspatial filter and order 0 for source-noise compensation.

[0496] Directing one or more of the grating orders to one or morecompensation detectors, such that the reflection from the surface isblocked by a polarizer, as explained in detail with respect to FIG. 19D.

[0497] The output of the compensation detector is amplified (orattenuated) so that the resulting difference signal is as close to zeroas possible when the surface is not moving relative to the device (orwhen the “window” is closed with an opaque cover), thus compensating forlocal oscillator power fluctuations.

[0498] The detected intensity (and the resulting detected signal) asdescribed in Eq. (8) includes a local oscillator component E_(LO) ² (=E₀²), a cross term, E₀E_(r), and a second order surface reflection termE_(r) ².

[0499] In order to compensate for variations in the E₀ multiplier of theE_(r) component, the signal from the compensation detector may be thecontrol voltage of a gain-controlled amplifier in one of the stages ofthe signal amplification (after the first compensation by subtractingthe E₀ ² component). The gain should be approximately proportional tothe inverse of the square-root of the compensation signal.

[0500] Preferably, for highest signal quality, the E_(r) ² component isalso compensated. This may be especially useful for those embodiments ofthe invention utilizing an “effective pinhole” (described below) tospatially filter the reflected surface illumination. In this embodimentthe exposed detector area over which the E_(r) ² component is integratedmay be much larger than the “effective pinhole” area. The E_(r) ²component can be compensated utilizing a detector that does not detect alocal oscillator field. The compensation detector may be positioned suchthat essentially no grating order falls on it. Alternatively, it maydetect only polarized light such that any local oscillator field iseffectively blocked. This may be implemented, for example, by placing apolarizer before the detector.

[0501] Changes in the E_(r) ² component are generally caused by changesof contrast in the surface, due for example to differences in thereflection coefficient of different colors. However, the reflection of ahighly reflecting surface (e.g., laminated paper) is also sensitive tosmall changes in the reflection angle near the angle of specularreflection, as presented in FIG. 26A. For simplicity of presentation,FIGS. 26A-26C show perpendicular illumination of a grating 830 from asource 832 and only one detector 834, in addition to a surface 836. Inorder to reduce the changes in the E_(r) ² component, it is preferableto arrange the source and the detectors so that the detectors arepositioned far from the specular reflection of the surface, as in FIG.26B. Alternatively, specular reflection from the surface toward thedetectors can be avoided by tilting the whole component by a few degreeswith respect to the surface plane, opposite to the detector directions,as in FIG. 26C. However, the effect of the tilt angle on the Dopplerfrequency should be taken into account. Preferably, Z-compensation (suchas described with respect to FIG. 21) is used to significantly reducethe sensitivity of the measurement to the accuracy of the tilt angle.

[0502]FIG. 3A shows a preferred implementation of a translationdetector, in accordance with a preferred embodiment of the invention, inwhich zeroth order detection is used and which does not incorporatedirection detection, or in which the detection of the direction is basedon an asymmetric grating transmission pattern and appropriate signalanalysis. FIG. 3A shows an integrated optical chip translation device 30that is suitable for mass production. It utilizes only a few componentsthat can be manufactured in large quantities for a low price. Device 30comprises a laser diode 32, preferably a single transverse mode laser.Laser light from laser diode 32 is preferably collimated by a lens 34,which is preferably a diffractive collimating lens, etched into ordeposited onto the surface of an optical chip substrate 36 of glass,quartz or the like, preferably coated with non-reflective layers on bothsides other than in designated areas. A grating 38 which may be anamplitude and/or a phase type grating, is mounted on optical chipsubstrate 36. Grating 38 is preferably etched or deposited onto thelower surface of substrate 36. Light reflected by the grating and lightreflected from a surface 42 are reflected by two reflective surfaces 40and 41 and focused by a lens 44, preferably a reflective diffractivefocusing lens, etched into the surface of optical chip substrate 36. Thelight is further reflected by a reflective surface 45. A pinhole 46,formed in a reflective/opaque layer formed at the focus of lens 44,passes only a plane wave from surface 42 and the reflected light fromgrating 38 to a detector 50, for example a PIN photo diode or similardevice. A compensation detector 52 is preferably placed behind lens 44and detects a portion of the light reflected by grating 38. A controller54, comprising a laser diode driver/modulator for activating laser diode32, detection amplifiers and zero crossing counting circuits orfrequency detection means is used for determining the translation or thevelocity of the surface. Compensation detector 52 supplies acompensation signal proportional to the amplitude of the localoscillator for reducing any residual effects of variations in the laseroutput. For reduction of noise, twisted wire pairs, shielded wires orcoaxial cable are preferably used to carry signals to and fromcontroller 54. Preferably, the apparatus is provided with legs or a ringsupport 56 or other such means on which the device rides on surface 42to avoid damage to grating 38 and to keep the distance between thegrating and the surface fairly constant.

[0503]FIG. 3B shows an alternative preferred embodiment of the inventionincluding direction detection by phase shifting of the local oscillatorand utilizing first order diffraction from the grating. Elements, whichare functionally the same are given the same reference numerals in bothFIGS. 3A and 3B. FIG. 3B shows a device 60 in which light from laserdiode 32 is collimated by a lens 62, to strike a grating 38. Grating 38is preferably mounted on a piezoelectric ring 64 (which is in turnmounted on optical substrate 36). Excitation of ring 64 adds a variablephase to the local oscillator (the light diffracted from grating 38) inorder to allow for direction detection, as described above. In theembodiment shown in FIG. 3B, both the detection of the signals used fortranslation and direction detection on the one hand and for compensationdetection on the other hand, are based on first order diffraction bygrating 38, but with opposite sign. Preferably, anti-reflection coatingsare used, where appropriate, to reduce unwanted reflections.

[0504] An integrated optical chip is the preferred implementation schemesince it can be manufactured in large volumes for a low cost. The figureshows only one detector for a single direction, with preferably a seconddetector measuring the orthogonal direction. All of the opticalelements—lenses, grating, mirrors and pinholes—are etched into ordeposited onto the optical substrate and are either reflective ortransmissive according to functionality. The discrete components in thesystem—laser diode, detector and piezoelectric transducer—are mounted ontop of the chip. The electronic elements of controller 54 may also bemanufactured or placed on top of the chip.

[0505] It should be understood that the features of FIGS. 3A and 3B canbe mixed and combined. For example if, in FIG. 3A, grating 38 is mountedon a transducer such as ring 64, then the result would be a deviceoperating in the specular reflection (zeroth order) mode with increaseddynamic range and possibly additional axial translation detection.Furthermore, it is possible to use an asymmetric grating in place ofgrating 38 and ring 64 of FIG. 3B for the purpose of directiondetection. For these and other preferred embodiments of the invention,combining various aspects of the invention will occur to persons skilledin the art.

[0506]FIG. 3C shows yet another method of determining direction, inaccordance with a preferred embodiment of the invention. Device 70 ofFIG. 3C is similar to device 60 of FIG. 3B except that grating 38 isplaced at the lower surface of chip 36 and a birefringent plate 66replaces piezoelectric ring 64. Source 32 produces linearly polarizedlight having a polarization that is at an angle of 45 degrees with thebirefringent axis of plate 66. Radiation that is reflected from thesurface passes through plate 66 twice and consists of two waves, eachhaving a polarization direction at a 45 degree angle with that of theradiation reflected from or diffracted from grating 38. These waves arealso ideally at a 90 degree phase difference with each other.

[0507] In addition, a polarizing beam splitter 68 is preferably placedbefore detector 50. Its axis is such that one polarization istransmitted toward detector 50 and the orthogonal polarization isreflected to a detector 67. In addition, beam splitter 68 directs halfthe radiation reflected or diffracted from grating 38 to each ofdetectors 50 and 67. The resulting signals detected by detectors 67 and50 will have a phase difference of 90 degrees. The sign of the phasedifference can be used to determine the direction of motion.

[0508] Alternatively, a partially reflecting mirror is used to separatethe radiation into two parts, and orthogonal polarizers are placed infront of the two detectors to separate the polarizations.

[0509] Preferably, the illumination of the grating is collimated.However, non collimated illumination may also be used, in which case thediffraction from the grating will be astigmatic (i.e., will no longerhave a single focal plane). It is preferable to compensate for thiseffect so that the spatial filtering is optimal. Conveniently, one ormore lenses may be designed to correct for the grating astigmatism.Alternatively or additionally, the grating itself may be designed toinclude astigmatic correction. Similar astigmatic effects andcorrections are expected to exist in other diffractive elementsilluminated by non-collimated light.

[0510] While the present invention is described above in variousembodiments for solving the general problem of translation measurement,the methodology is applicable to a large number of products. Oneparticular application of the optical translation measurement method ofthe invention is a novel optical cursor control device (mouse) whichderives its translatatory information from movement on substantially anydiffuse surface, such as paper or a desktop. One design for such adevice, in accordance with a preferred embodiment of the invention, isshown in FIG. 4. An optical mouse 80 comprises an “optical chip” 82which is preferably a device such as device 30, device 60, device 70 ora variation of these devices. Chip 82 is mounted in a housing 84 andviews paper 42 through an optical aperture 86 in housing 84. Input andoutput leads from chip 82 are preferably connected to a printed circuitboard 88 or the like on which are mounted electronic circuitry 90corresponding to the controller of devices 30, 60 or 70. Also mounted onPC board 88 are one or more switches 92 that are activated by one ormore push-buttons 94 as in conventional mice. The mouse isconventionally connected to a computer via a cable 96 or with a wirelessconnection.

[0511] The method of measurement in accordance with preferredembodiments of the invention described above allows for a wide dynamicrange of translation velocities, covering all the required range fornormal operation of a mouse. Such a device can be characterized as a‘padless optical mouse’ to provide orthogonal signals to move a cursorfrom position to position on a display screen in response to movement ofthe mouse over any sufficiently diffusely reflective surface, such aspaper or a desk top. Thus, special contrasting markings or specialpatterns are not necessary.

[0512] Mouse systems usually use mechanical transducers for themeasurement of hand translation over a surface (commonly a “mouse pad”).A need for moving-parts-free, reliable and accurate translationmeasurement technology for use in mouse systems is well acknowledgedtoday. A few optical devices were developed, but still suffer fromvarious deficiencies, such as a need for a dedicated patterned pad, lowtransducing performance or high cost.

[0513] An optical padless mouse according to one preferred embodiment ofthe invention can be used in two ways, according to the user'sconvenience. It can be used as a “regular” mouse, whereby the mouse ismoved on top of a surface, and its motion relative to that surface ismeasured. It can also be flipped over, if so desired, and instead usedby moving the finger along the device aperture. The motion of the fingerrelative to the mouse body, which is now stationary, will be measured.

[0514] One such device 100 is shown in FIGS. 5A and 5B. FIG. 5A showsthat structurally the device is similar to that of FIG. 4 (and the samereference numbers are used in the two Figs. for ease of comparison),except that buttons 94 are on the side of housing 84 in device 100. Inthe mode shown in FIG. 5A, device 100 is stationary and is used to trackthe movement of finger 102 of an operator. It should be clear thatdevice 100 can be turned over and used as a mouse, in much the same wayas the mouse of FIG. 4. FIG. 5B shows a perspective view of the device,showing an optional switch 104 which is used to indicate if device 100is used as an ordinary mouse or in the mode shown in FIGS. 5A and 5B.Alternatively, such a switch may be a gravity switch mounted in thedevice to automatically switch modes. It is generally desirable to knowin which mode the device is operating since the direction of motion ofthe cursor is opposite for the two modes and usually, the sensitivitydesired is different for the two modes.

[0515] Furthermore, using a translation measurement device with a smallaperture, as in the present invention, and moving a finger along itsaperture, enables moving a cursor through measurement of the translationof the finger, much like a touch pad. This function may be termed“touch-point” and may be used in dedicated minute locations on keyboardsas well. This device would be identical to the device of FIG. 5 exceptthat the optical chip would be mounted in the keyboard as would theswitches. Also, an OTM “touch-point” may be used on the top of the mouseas an alternative to a scrolling wheel. “Clicks” may be detected, forexample, by bringing the finger into and out of range of the touchpoint.

[0516] This device can be used to replace pointing devices other than amouse, for example, pointing devices used in laptop or palmtopcomputers. Virtually any one or two dimensional motion can be controlledusing such a device.

[0517] Currently, laptop computers pointing devices employ either atrack ball, a touch pad, a trackpoint (nipple) or an attached mouse.These devices carry diverse drawbacks. In particular, the track ballcollects dust much like a regular mouse, the touch pad is sensitive todampness and was hailed unfriendly by many users, the trackpoint driftswhen it should be idle and the attached mice are delicate and require adesktop to work on.

[0518] The touch-point device is small in size, its working aperture canbe less than 1 mm² and it provides high resolution and dynamic range.This makes it an ideal solution as a pointing device to be embedded in alaptop computer. The device is operated by moving a finger across theface of the aperture, in a somewhat similar manner to the use of a touchpad. The difference being, that the aperture is very small in sizecompared to the touch pad, it is free of problems like humidity anddampness and its reliability is expected to be high. In fact, severaltouch point devices can be easily embedded in a single laptop or a palmtop, including on keys, between keys, or next to the screen.Additionally, a pressure sensitive device may be included under thetouch point device and the sensitivity of the touch point maderesponsive to the pressure of the finger on the touch point.

[0519] In a preferred embodiment of the invention, two touch points areprovided, a first touch point and circuitry which moves a pointerresponsive thereto and a second touch point and circuitry which causesscrolling responsive thereto.

[0520] In a further preferred embodiment of the invention, the presentinvention can be used as an improved translation and/or velocitymeasurement system for a scanning-pen, capable of scanning lines of text(or any other pattern) and storing them, for downloading later to a PC,and/or for conversion to ASCII code using OCR software. An example ofsuch a device is shown in FIG. 6. A scanning pen 120 comprises a‘reading’ head with a one dimensional or two dimensional array of photodetectors (such as a CCD array) 122 and a lens 123, wide enough to scana typical line height, and a lighting source 124 as in conventionallight pens. The pen head also contains an optical translationmeasurement system 82 in accordance with the invention, for one or twoaxis measurement of the translation of the pen head across the scannedpaper and possibly another one to extract rotation information. The pencan then either store the scanned line as a bitmap file (suited forhand-writing, drawings etc.) or translate it immediately through usinginternal OCR algorithm to binary text. The stored information may bedownloaded later to a computer, palmtop or phone, etc. For this purposeand for the powering and control of the various devices in pen 120, itis provided with a controller or microprocessor 128 and batteries 129.

[0521] Optical translation methods of the present invention allow fordevices to be small in size, convenient to use, and accurate. The highaccuracy results from the inherent high accuracy of the method of theinvention as compared to current mechanically-based mice and from theease of measurement in two or three dimensions. Similar commercialdevices today use a patterned wheel that is pushed against the scannedsurface while scanning and rolled in order to measure the translation bydetecting the rolled angle of the wheel. This technique only detects thelocation along the line and not along its vertical axis and itsrelatively low accuracy limits the range of applications it can be usedfor.

[0522] A further preferred application of the optical translation methodand device of the present invention is a portable or a fixed device, forscanning signatures and relaying them to an authentication system.Similar in principal to the scanning pen, the signature reader containsa ‘reading’ head, with a one dimensional or two dimensional array ofphoto detectors (such as a CCD array). It has an aperture wider thanthat of the scanning pen, to be able to read wider or higher signaturesand contains an optical translation measurement device, for detection ofthe two axes translations of the hand or instrument which is moving thedevice across the scanned signature. The signature reader does notcontain any OCR, as no text files are to be created. Instead, it isconnected (through direct, hardwire line or wireless link, or through anoff-line system), to an “authentication center”, where the scannedsignature is compared to a “standard signature” for validation. Thisdevice can be accurate, while cheap, small and easy to use.

[0523] A still further application of the devices and methods describedabove is in the field of encoders. The present invention can replacelinear encoders and angular encoders, which generally require highlyaccurate markings on either an encoder wheel or on a surface, by asubstantially markless encoder. An angular encoder 130 in accordancewith this aspect of the invention is shown in FIG. 7. Encoder 130comprises a disk having a diffusely reflecting surface 132 mounted on ashaft 131. It also includes an optical chip 82 and controller 90,preferably essentially as described above. Preferably, surface 132 ismarked with one or two radial marks 136 to act as reference marks forthe encoder and for correction of errors, which may occur in reading theangle during a rotation. This mark may be read by optical chip 82 or byusing a separate detector.

[0524] The motion of the surface illuminated by chip 82 may be describedas a combination of a common translation of all scatterers according tothe tangential motion at the illuminated portion and a rotational motionaccording to the angular velocity of surface 132. Preferably, theilluminated area is small compared to the distance from the center ofrotation such that the curvature induced component may be neglected.Alternatively, in a non-Doppler mode of operation, a grating with equalangular spacing between grating lines is preferably used, enablingdirect measurement of the angular displacement instead of measurement ofthe equivalent surface translation.

[0525] A further embodiment of the invention is a virtual pen, namely apen that translates movement across a featureless page into positionreadings. These position readings can be translated by a computer intovirtual writing, which can be displayed or translated into letters andwords. The computer can then store this virtual writing as ASCII code.Transfer to the computer may be either on line (using a wired orpreferably a wireless connection to the computer) or off-line whereinthe code or positions are stored in the “pen” and transferred afterwriting is completed. This embodiment of the invention provides acompact, paper-less and voice-less memo device.

[0526] In a typical fax/printer, the paper is moved in a constant speedrelative to the writing head with an accurate motor. The head releasesthe printed data line by line, in a correlated fashion with the speed ofadvancing paper. This method is both expensive, as it requires anaccurate motor and mechanical set up, and inaccurate, as the papersometimes slips in the device, thus the paper translation is not wellcorrelated to the printing device, resulting in missed or crooked lines.

[0527] With an optical translation measuring device, it is possible todetect paper slippage by measuring the paper advancement on-line. Theprinting device is then coordinated with the actual translation of thepaper, thus creating a highly accurate and economic system. Similarly,these principles can be applied to a desktop scanner, where a readinghead replaces the printing head. Furthermore, the type of paper or othersurface (for example, type of cloth) may be identified fromcharacteristics of the detector signals. Features, which may be used toidentify the type of paper, include the ratio between reflected AC andDC power, absolute AC and DC power, harmonics ratio, etc., or acombination of these characteristics. In addition, the sensor may detecta discontinuity in paper height, amounting to multiple feed situation.This discontinuity may be determined by an axial translationmeasurement, an apparent discontinuity in the measured transversedirection, or loss of signal caused by temporary loss of coherencebetween the reflection and the local oscillator.

[0528]FIG. 8 is a schematic of a motion sensor useful in a scanner, faxmachine or printer in which motion is only in one direction. Motiondetector 200 includes a source 202 that is fed to a housing 204 by afiber optic cable 205. The output of cable 205 is collimated by lens 206and illuminates a moving surface 208, through a grating 210. Lightreflected from grating 210 and surface 208 is collected by a fiber opticcable 212 which is placed at the focal point of lens 206. The output ofcable 212 is fed to a detector 214, for further processing as describedabove.

[0529] In a preferred document scanner embodiment of the invention, themotion detector measures the relative movement of a document,preferably, without utilizing any printing on the document, while areading head reads printed information from the document. A memoryreceives information from the printing head and stores it in memorylocations, responsive to the measurement of movement of the document.

[0530] In a preferred printer embodiment of the invention the motiondetector measures the movement of a sheet on which markings are to bemade and a memory transmits commands to mark the paper, in accordancewith information in the memory, responsive to the measurement of motionof the paper.

[0531] Either or both preferred scanner and printer embodiments of theinvention may be utilized in a facsimile machine in accordance withpreferred embodiments of the invention.

[0532] Motion detectors of the invention may also be used to measure thevarious motions in CD and magnetic memories.

[0533]FIG. 9 is a simplified block diagram of typical electroniccircuitry 140 useful in carrying out the invention. A “primary”photodetector 142 (corresponding, for example to detector 50 of FIGS. 3Aand 3B) receives light signals as described above. The detector detectsthe light and the resulting signal is preferably amplified by anamplifier 144, band pass filtered by a filter 146 and further amplifiedby an amplifier 148 to produce a “primary” signal. A compensating signalis detected, for example, by photodetector 150 (corresponding todetector 52 in FIGS. 3A-3C) and is subtracted (after amplification, byamplifier 152 and band-pass filtering by filter 154) from the “primary”signal in a difference amplifier 155 to remove residual low frequencycomponents in the primary signal. Preferably, band pass filters 154 and146 are identical. The resulting difference signal is amplified by avoltage controlled amplifier 156 whose gain is controlled by the outputof a low pass filter 153 (which is attenuated by an attenuator 158optionally adjusted during calibration of the system). The output ofamplifier 156 is fed to a zero crossing detector and counter 160 anddirection control logic 162, which determine the direction oftranslation of the surface. Where a piezoelectric element 64 (FIG. 3B)is used, a control signal corresponding to the frequency of displacementof the of the element is fed to the direction control logic 162 where itis subtracted from the zero-crossing detector count.

[0534] For preferred embodiments of the invention, the wavelength of thelaser source is preferably in the infra-red, for example 1550nanometers. A spectral width of 2 nanometers is typical and achievablewith diode lasers. A source power of 5 mW is also typical. A gratingopening of 1.5 mm by 1.5 mm and a grating period of 150 lines/mm arealso typical. The laser source output is typically collimated to form abeam having a diameter of somewhat less than 1.5 mm and is typicallyincident on the grating at an angle of 30 degrees from the normal. Theoptical substrate may have any convenient thickness. However a thicknessof several mm is typical and the focal length of the lenses used isdesigned to provide focusing as described above. Typically, the focallength of the lenses are a few mm. Typically, pinhole 46 (FIGS. 3A-3C)has a diameter of several micrometers, typically 10 micrometers. Itshould be understood that the above typical dimensions and othercharacteristics are provided for reference only and that a relativelywide variation in each of these dimensions and characteristics ispossible, depending on the wavelength used and on other parameters ofthe application of the optical chip.

[0535] In some preferred embodiments of the invention the pinhole isomitted and is replaced by an “effective pinhole.” This effectivepinhole is achieved by focusing a local oscillator field, as for examplelight reflected or diffracted from a grating, on the detector. In thisway, amplification of the field reflected from the surface is achievedonly at the focus of the local oscillator field. Thus for example,pinhole 46 in FIGS. 3A, B and C may be removed and the local oscillatorfield focused on the detector surface.

[0536] The intensity profile of the focused local oscillator fielddetermines the amplification of signal fields at the same location onthe detector. Thus, where the intensity is high the amplification issignificant, whereas low local oscillator intensity results in lowamplification. The focused spot on the detector surface thus functionsin the same manner as a real pinhole in a ‘standard’ spatial filter. Thequality of the local oscillator beam spatial profile—how close it is tobeing diffraction limited—determines the quality of the resultingspatial filtering. A diffraction limited local oscillator field focusedon the detector utilizes the maximum amount of power for amplificationof the signal, and is not sensitive to angular misalignments like a realpinhole. Elimination of the physical pinhole in this manner results in amore robust arrangement having lower sensitivity to mechanicalvibrations, broad tolerances on angular alignment and higher overallamplification. The signal light that is not amplified is not rejected,as with a pinhole, but, with a local oscillator field much stronger thanthe signal field, its effect on the measurement is negligible. The samearrangement is also relatively insensitive to focusing errors.

[0537] Utilizing an effective pinhole arrangement in Dopplermeasurements with a grating, in which the direction of the localoscillator field is dependent on wavelength, has the advantage of notbeing sensitive to wavelength variations of the source. A change inwavelength causes a corresponding change in the reflection angle fromthe grating, so that the local oscillator image on the detector moves.If a real pin-hole is used, this affects the measured amplitude of thesignal and may even result in a total loss of signal. With an effectivepinhole the measured signal is not affected as long as the focal pointis on the detector. Moreover, the detector signal is wavelengthindependent in a grating-reflector configuration and is a function ofthe translation, grating period and order of local oscillatorreflection, as described above with respect to the grating basedsystems.

[0538] A preferred embodiment of an arrangement where the focusing isdirectly onto the detector is shown in FIG. 10. FIG. 10 shows (forsimplicity of explanation) a one dimensional sensor without directiondetection packaged in a standard electronics package (TO5 or the like).The sensor includes an at least partly coherent radiation source such asa laser diode 250, a lens 252, grating 254, a detector (for example, aPIN diode) 256, a housing 258, exit leads 260 and electronics 262. Laserdiode 250 and detector 256 are preferably optically on the same plane,which is also preferably the focal plane of lens 252. The zero orderreflection of the laser from grating 254 is focused onto the surface ofdetector 256 and serves as a local oscillator. If the distance of laserdiode 250 and detector 256 from the lens are different, the arrangementis such that the laser image is focused by the lens onto the detectorsurface, as described above in detail with respect to the embodimentwhich utilizes a non-collimated source and a matching spatial filter.While no direction detection is shown in FIG. 10 and in some of thesucceeding embodiments, direction detection as described above (orbelow) may be adapted to these embodiments.

[0539] The operation is similar for sensors using first (or higher)order diffraction as the local oscillator field. The arrangement isslightly different. One such arrangement, in accordance with a preferredembodiment of the invention, is shown in FIGS. 11A and 11B. The sensorshown is a two dimensional sensor without direction detection, andincludes a source of radiation such as a laser diode 270, a lens 272, atwo dimensional grating 274, a pair of detectors 276 and 278, a housing280, exit leads 282 and electronics 284. As in the embodiment of FIG. 10laser diode 270 and detectors 276 and 278 are preferably in the sameoptical plane. FIG. 11B shows a planar view of the plane of detectors276 and 278 and source 270 as seen at section XIB-XIB. Detector 276functions as an X axis detector and detector 278 as a Y axis detector.The first order diffraction from grating 274 in the X direction isfocused onto X detector 276 while the first order diffraction in the Ydirection is focused onto Y detector 278.

[0540] Preferred embodiments of the invention that utilize an effectivepinhole are easier to align and, when manufactured as an integratedoptical block, have looser tolerance requirements. This is especiallytrue when the local oscillator is derived from light diffracted from agrating at non-zero order since for this case the placement of thepinhole depends on wavelength. Thus, the wavelength stability of thesource of illumination is much relaxed when a effective, rather than aphysical pinhole is utilized.

[0541] In some preferred embodiments of the invention alternativemethods of determining the direction of motion are utilized. Inpreferred embodiments of the invention, which provide these alternativemethods, mechanical motion of an optical part is utilized to determinethe direction of motion. In some preferred embodiments of the inventiontwo detectors are provided and motion in one direction causesillumination of one of the detectors by light reflected or refractedfrom the grating. Two preferred embodiments of the invention, whichprovide direction detection utilizing this principle, are shown in FIGS.12A-12B and 13A-13B.

[0542]FIGS. 12A and 12B illustrate the principle of one of theembodiments. These Figs. show a sensor 290 that includes a source of atleast partly coherent radiation such as a laser diode 292, a lens 294, adetector 296, a second detector 298 and a pair of gratings 300 and 302.Gratings 300 and 302 are mounted on the surface of a bi-stable wedgedelement 304. Motion of the sensor in one direction causes element 304 totake the position shown in FIG. 12A, such that radiation is reflected orrefracted from grating 300 to detector 296. Friction of element 304 withthe surface whose motion is being measured, when the sensor is moved inthe other direction, turns element 304 to the position shown in FIG.12B. In this configuration, radiation is reflected or refracted fromgrating 302 to detector 298. The direction of motion is thus determinedfrom which of the detectors produces a signal.

[0543] An extension of this embodiment to two dimensional operation isprovided by replacing element 304 by a 4-faced pyramid operating in asimilar manner, with corresponding 4 detectors, where the gratings aretwo dimensional.

[0544]FIGS. 13A and 13B show a second embodiment of a mechanicaldirection detection method, using two adjacent gratings. As in FIGS. 12Aand 12B the embodiment comprises a source of at least partly coherentradiation such as laser diode 292, lens 294, detectors 296 and 298. Theembodiment also includes two gratings 310 and 312. Each of gratings 310and 312 has two parts with different periodicity, for example 150 lp/mmon their left halves and 170 lp/mm on their right halves. The bottomgrating is shifted by the friction with surface 42, and moves to apre-defined stop in the direction of motion. The two halves of thegratings are arranged such that the motion will cause one grating halfto be blocked (i.e., the reflecting portion of one of the gratingscovers the openings in the other), while the grating on the other halfwill become visible (i.e., the metal portions coincide), although notgenerally with a 50% duty cycle. Motion in the opposite directionexchanges the role of the two grating halves, thus enabling a differencein reflection angles between the two directions and illumination ofdifferent detectors. The two configurations are depicted in FIGS. 13Aand 13B, respectively. The direction of motion is determined from whichof the detectors produces a signal.

[0545]FIGS. 13C and 13D show another system for switching from onegrating to another. In these figures only the gratings themselves areshown. An upper portion comprised of reflecting elements 400 does notmove with respect to the detector. A lower portion comprises alternatingsections 401 and 402 that are gratings having different periods. In theposition shown in FIG. 13C elements 400 block grating sections 401 suchthat light incident on the gratings is directed at one angle, determinedby the period of grating sections 402, which is visible to the incidentradiation and which partially transmits it. In a second position, towhich the lower portion is moved by friction with the surface whosevelocity is being measured, elements 400 block grating sections 402 andexpose sections 401 such that incident light is directed at an angledependent on the period of grating 401. This allows for switching of thedetectors, which receive the light, as in FIGS. 13A and 13B.

[0546] The principle of this embodiment of the invention can be extendedto two dimensions by replacing the gratings with two dimensionalgratings divided into quarters based on the same principle shown inFIGS. 13A and 13B.

[0547]FIG. 14 illustrates the principle of another embodiment of aDoppler based sensor system for measuring the velocity of a surface.Unlike the sensors described above, this sensor does not require the useof a grating. A collimated, at least partially coherent light source 320illuminates an optical element 322 having a first plane 324 adjacent toand oriented at an angle to surface 42 and a second plane 325 parallelto surface 42. Light reflected from plane 324 (which is preferablyreflection coated), is focused by a lens 326 on a detector 328 andserves as a local oscillator. Part of the light reflected by surface 42is also focused on detector 328 and coherently interferes with the localoscillator field. The light reflected from surface 42 toward detector328 is Doppler shifted by the translation of the surface. Thus, thedetector signal includes an oscillating component indicative of thetranslation of surface 42. It should be noted that surface 325 plays nopart in the detection process. Furthermore, it should be noted that allof the components may be mounted on optical element 322 to form anintegrated sensor. Extension to 2-D measurement is achieved using twoslanted planes and two detectors.

[0548] In accordance with some preferred embodiments of the inventionthe reflector from which the local oscillator field is reflected is notadjacent to the surface whose velocity is being measured. Two preferredembodiments of the invention, which embody similar principles, are shownin FIGS. 15 and 16.

[0549]FIG. 15 shows a sensor including an at least partially coherentlight source, such as a laser 350, an optical medium 352 having apartially reflecting and partially transmitting surface 354 and atotally reflecting surface 356. The sensor also preferably includes alens 358 which collimates source 350 and a spatial filter embodied inthis embodiment by a lens 360 which focuses the light on a detector 362and signal processing electronics 364. The focused light acts as aneffective pinhole, as described above. The light source provides atleast partially coherent radiation, which is directed toward surface 42.

[0550] The light from the source is split by surface 354 into one beamreflected from surface 352 toward surface 356 and one beam transmittedtoward the surface 42. The light that is reflected from surface 42 istransmitted through surface 354, toward the detector 362. The light thatis reflected from surface 354 is totally reflected from surface 356,such that a third reflection of it from surface 354 is also directedtoward detector 362. The optical path length difference for lightpropagating in the medium by multiple reflections (local oscillator) andlight reflected from surface 42 towards the detector should be withinthe coherence length of the source. Translation of the surface resultsin an oscillating detector signal indicative of the amount oftranslation as in the previously described embodiments. In alternativepreferred embodiments of the invention, Surface 354 may be a gratingwherein the local oscillator is derived from light diffracted from it atone of its diffraction orders. For this situation, surface 354 need notbe at an angle to surface 42.

[0551] Although surface 356 is preferably totally reflecting, it may bepartially transmitting or partially absorbing. This reduces the localoscillator signal. If surface 356 is partially transmitting, the lightpassing through it may be used to measure the intensity of the lightsource using another detector, and subsequently compensate for amplitudemodulation of the source intensity in order to improve the performanceat the low end of the velocity range as described above in conjunctionwith FIGS. 3A and 3B.

[0552] According to a preferred embodiment of the invention, the regionbetween surface 354 and surface 42 is filled with a second opticalmedium to improve the flatness of surface 42 (if it is non-rigid, e.g.—apaper) and to prevent dirt accumulation.

[0553] According to another preferred embodiment of the invention shownin FIG. 16, a sensor is fabricated utilizing a modified cubic-shapedbeam-splitter. A preferably collimated, at least partially coherentlight source, such as a laser 380 is directed toward a partiallyreflecting, partially transmitting surface 382. Light transmittedthrough surface 382 is directed toward surface 42 and from surface 42 is(partially) reflected from surface 382 to a detector 384 (via focusingoptics 386). Light reflected by surface 382 is directed toward areflector 388 and from there (through surface 382) to detector 384.Thus, the beam splitter acts as an interferometer such that atranslation of the surface 42 relative to the device and parallel to thesurface introduces a Doppler shift between the reflection from reflector388 (serving as a local oscillator) and reflection from surface 42.

[0554] Thus, light that is reflected from surface 42 and light that isreflected from reflector 388 interfere on detector 384. The opticalmedium is scaled such that the optical path length difference of thesetwo light waves is within the coherence length of source 380.

[0555] The arrangement is such that the partially reflecting interface,the totally reflecting interface and the surface are not all parallel toeach other. Thus, the detector signal includes an oscillating componentdue to a Doppler phase shift of the light reflected from the surface,that is representative of the surface translation relative to theoptical device and parallel to the surface.

[0556] Preferably, the light from source 380 is collimated. Preferably,the light reaching detector 384 is focused onto the detector surfacesuch that a point-image of source 380 is formed thereon.

[0557] Two dimensional translation measurement may be achieved by usingorthogonally tilted, partially-reflecting, interfaces or orthogonallytilted, totally-reflecting, surfaces.

[0558] The Doppler shift of the light that is reflected from surface 42is proportional to the component of relative velocity between the sensorand surface 42 along the bisector between the light beam incident on thesurface and the portion of light reflected from it that is collected bythe detector. The Doppler shift is inversely proportional to the lightwavelength. Preferably, the optical medium is selected such that therefractive index dispersion induces a change in the bisector angle withrespect to the surface plane that compensates for the effect of thechange in wavelength on the Doppler shift. Thus, the measurement errordue to the finite spectral width of the source and its wavelength driftsis substantially reduced.

[0559] The method shown in FIGS. 15 and 16 and its embodiments providesfor relatively cheap, robust, alignment-free and accurate apparatus fortranslation measurement of rough surfaces moving parallel to thesurface. The method is applicable to a wide range of applicationsutilizing translation measurement, as described with respect to theother embodiments of the invention.

[0560]FIG. 17 shows another preferred embodiment of the invention. Theembodiment of FIG. 17 provides for enforcement of a specificpolarization on the reflection from the surface. FIG. 3C illustrates amethod for determining the direction by providing a differentpolarization for the light reflected from surface 42 and the localoscillator. A phase shift is provided by placing a birefringent plate inthe path of the radiation to and from the surface. However, this methodis based on the assumption that when the light is reflected from thesurface, its polarization is preserved. Often this is not the case, andthe quadrature signal that is supposed to be generated by the detectorsdeteriorates and can even switch sign for the same motion direction.

[0561] An additional linear polarizer between the birefringent material(“quarter waveplate”) and the surface enables the measurement to beinsensitive to the surface characteristics. The polarizer enforces itslinear polarization direction on the reflection from the surface,irrespective of the surface characteristics. By placing the polarizeraxis at 45 degrees to the birefringent material axes, the reflection issubsequently circularly polarized by the birefringent layer when passingthrough it towards the detectors. Thus, precise quadrature signal isensured for the 2 cross-polarized detectors even when the surface itselfis not polarization preserving.

[0562] Another property of this arrangement is the ability to place thebirefringent layer “on-top” of the grating (instead of between thegrating and the surface). The local oscillator light experiences doublephase shift (for quarter waveplate, it sees a half wave retardation)while the surface reflection is shifted only once and thus enablesquadrature measurement.

[0563]FIG. 17 shows a first preferred embodiment of a motion detector500 that inter alia, includes this feature. Motion detector 500comprises a source of partially coherent light 502 that illuminates apreferably collimating lens 504. Light that exits below lens 504 ispreferably collimated (i.e., the light rays are all parallel). A quarterwave birefringent plate 506 and a grating 508 underlay the plate. Thelight reflected/diffracted from the grating experiences a 180-degreephase shift between its orthogonal components due to its passing twicethrough the birefringent plate. While plate 506 and grating 508 areshown as separate elements, they may be combined into a single element,for example by depositing or embossing the grating on the surface of thebirefringent plate.

[0564] A linear polarizer 510 preferably underlies the grating. Lightthat is reflected from a surface (not shown) underlying the polarizerthat passes through the birefringent plate a second time will becircularly polarized. However, since the light passes through polarizer510 a second time before reaching plate 506, the polarization isenforced and “contamination” of the measurement is avoided.

[0565] Light diffracted from the grating at an angle determined by thegrating line spacing and order of diffraction and light diffuselyreflected from the surface are incident on a detection module 512.Detection module 512 includes a phase grating 514 that splits theincident radiation into two preferably equal parts and sends them via apair of polarizers 516 and 518 to a pair of detectors 520 and 522,respectively. Polarizers 516 and 518 are aligned at 90 degrees withrespect to each other and are aligned to provide preferably equalstrengths of grating diffracted radiation at each of the detectors.Detection module 512 performs the same function as elements of FIG. 3C.That is, detection module 512 splits the circularly polarized wave(based on the surface reflection) into linear components and each ofthem separately interferes with a portion of the wave diffracted bygrating 508. The diffracted wave, having a linear polarization at 45degrees to the direction of polarization of each of the polarizers, isalso split by the grating and detected, preferably equally, by thedetectors. The magnitude of the motion is conveniently determined fromthe number of zero crossings of the signals detected by the detectors(based on a Doppler shift), and the direction of the motion isdetermined based on the relative phases of these signals.

[0566] Detection module 512 utilizes a phase grating and two polarizersto split and direct the incoming waves to the detectors, rather than thepolarizing beam splitter of FIG. 3C. In practice, the embodiment ofmodule 512 is believed to be less expensive to produce. If a binaryphase grating (or a blazed grating) is used, then the system is not onlyinexpensive but also light efficient.

[0567] In a preferred embodiment of the invention, module 512 is mountedon a backplate or heatsunk substrate 524, together with source 502 andan electronics module 526. Electronics module 526 may contain acontroller to control source 502 and electronics that receives signalsfrom detectors 520 and 522. Preferably, electronics module 526 partiallyor fully processes the signals, as described above, to provideinformation to a computer or other device (not shown) regarding themagnitude and direction of the motion of the surface.

[0568]FIG. 18 shows another motion detector 530 generally similar instructure to that of FIG. 17. However, the detector includes a number offeatures that should be noted. For ease of description, those parts ofdetector 530 that are similar to those of detector 500 of FIG. 17 aremarked with the same reference numbers and are not further described.

[0569] In FIG. 18, the local oscillator is spatially separated from thesurface illumination and diffraction path. Furthermore, in FIG. 18, acut-out 532 is preferably provided to equalize the lengths of wave pathsfor the waves diffracted from the grating and reflected from the surfacewhose relative motion is to be measured. As will be recalled, coherencebetween these waves is preferred if not required at the detectors. Sincethe path of the wave reflected from the surface is longer than that fromthe grating, this places a strong coherence requirement on source 502.In a preferred embodiment of the invention, cutout 532 provides for areduction in optical path length for the wave reflected from thesurface, so as to match the path lengths.

[0570] The optical arrangement of separated local oscillator such asthat presented in FIG. 18 is also intrinsically suitable for having onlyone transmitted beam and no diffraction of the reflected surfaceillumination, desirable in the Doppler mode of operation. However, theseparation of the beam into one part serving as the local oscillator andanother part serving to illuminate the surface is more sensitive to thebeam quality and is less robust then schemes that uses most or all theillumination for both the local oscillator and the surface illumination.

[0571] While this cut-out may be useful for other preferred embodimentsof the invention, for example for the embodiment shown in FIG. 17, it isespecially useful when a protective, preferably scratch resistant layeror substrate 534 is provided adjacent to the surface. This substrateincreases the optical path length of the wave reflected from thesurface, without changing the optical path length of the wave diffractedfrom the grating. The provision of a protective layer is also applicableto many of the above-described embodiments. Furthermore, substrate 534or other parts of the optical path may be colored (i.e., spectrallyfiltering) to reduce the effects of stray light while passing the laserlight.

[0572] In the embodiment shown in FIG. 18, the structure for generatingthe reflected and diffracted waves is different from that shown in FIG.17. In FIG. 18, a phase grating 536 overlays a ⅛ wave birefringent plate538, which is in turn is underlain by a reflector 540. Preferably, thereflector is applied directly on plate 538. Since waves that arereflected from reflector 540 pass through the ⅛ wave plate twice, thereflected wave is circularly polarized. The reflection from the surfacepreferably passes through a linear polarizer 542 in both directions asit is reflected from the surface. Thus, this wave has an enforced linearpolarization. The operation of the rest of the system is the same asthat described for FIG. 17.

[0573] In alternative preferred embodiments of the invention, a quarterwave birefringent layer can be placed in the path of the beam emitted bysource 502, converting it to circular polarization. Thus, this layer maybe much smaller (and less expensive) than the comparable layer shown inFIGS. 17 and 18, which layers are then omitted. Furthermore, for thoseembodiments of the invention in which a birefringent plate is used, aplate resulting in elliptical polarization (rather than the circularpolarization described above) may be used.

[0574] In some preferred embodiments of the invention, a quarter wavelayer (from birefringent material such as quartz) may be deposited onthe emitting surface of an otherwise linearly polarized laser diode toproduce a circularly polarized beam. Preferably, the deposition is partof the process by which the diode is manufactured, e.g., thebirefringent layer is deposited on top of an outer Distributed BraggReflector of a Vertical Cavity Surface Emitting Laser. This scheme usesa much smaller amount of birefringent material, since the coated area isjust the area of the emitter. Moreover, a small birefringent layer canbe more accurately manufactured than a large one. An additional linearpolarizer, deposited under the birefringent layer forms an opticalisolator combination, attenuating stray light reflection back into thelaser cavity.

[0575] Similarly, in some preferred embodiments of the invention, linearpolarizers are incorporated into the surface of the detectors, ratherthan providing separate polarizers, when these are indicated as beingrequired in some of the above referenced embodiments of the invention.Use of such polarized detectors reduces the complexity of the assemblyof the motion detectors. Applying a polymer-based polarizer on top ofthe detector can be used to produce such detectors. Alternatively, thepolarizer may be manufactured by fine line grooving (with line widths onthe order of a wavelength) of a dielectric layer deposited on thedetector face.

[0576]FIGS. 19A and 19B show two integrated versions of motion detectorsbased on direction detection principles similar to those of FIGS. 3C, 17and 18.

[0577]FIG. 19A shows a motion detector 550 built on a block 552comprising a beam splitter 554 and two lenses 556 and 558. A laser diodesource 560 is mounted adjacent to lens 556, which collimates the lightemitted by the source. A collimated beam 561 impinges on beam splitter554, which splits the beam into a first part 562, which continues tosurface 12 and a second part 564, which is reflected to a ⅛ wave plate566 and a mirror 568. Beam 564, after passing twice through the plate iscircularly polarized, as it travels back toward beam splitter 554.

[0578] Beam 562 passes through a linear polarizer 570 and preferablythrough a protective layer 572 before being reflected back toward beamsplitter 554. The portion of reflected beam 564 passing through the beamsplitter and the portion of reflected beam 562 reflected from the beamsplitter are directed together toward lens 558, which focuses them. Asecond beam splitter 574, splits both beams and directs them topolarized detectors 576 and 578 (each having a polarizer 580 and adetector 582). The detectors are used to detect the frequency andrelative phase of the linear components of the beam reflected fromsurface 12, in essentially the same manner as described above withrespect to FIGS. 3C, 17 and 18.

[0579] It should be noted that the top of motion detector 550 is notsquare with the bottom so that the reflected beam is Doppler shiftedfrom the beam incident on surface 12. This Doppler shift (and its sign)is used to detect the motion. Furthermore, in preferred embodiments ofthe invention, the lenses are anti-reflection coated to avoid theeffects of multiple reflections.

[0580] A second integrated motion detector 590, shown in FIG. 19B, alsoembodies similar principles. All of the optical components of the systemare mounted on a block 592 in which a grating 594 is sandwiched.Preferably, the grating and top and bottom surfaces are parallel. Twolenses 596 and 598 having functions similar to those of lenses 556 and558 of FIG. 19A are preferably incorporated into block 592. In FIG. 19B,elements having similar functions to those of corresponding elements ofFIG. 19A are similarly numbered. A reference beam is reflected fromgrating 594 toward a back-mirrored ⅛ wave plate (566, 568) and thence,via a second reflection, toward lens 598. The beam passing through thegrating preferably passes through a linear polarizer and optionalprotective layer and is reflected toward lens 598. The detection systemoperates in a manner similar to that described above.

[0581]FIGS. 19C and 19D shows details of a detector module 610 for asystem in which a birefringent plate is used to affect one or both ofthe grating or surface reflected beams. Examples of such systems are themotion detectors described in FIGS. 17, 18 and 19A. In these motiondetectors, when the source is linearly polarized, the birefringent platemay be moved close to the detectors. In this case, the birefringentplate would be smaller than when it is placed elsewhere and can, in somepreferred embodiments of the invention, be integrated with the detectorsas described above for polarizers.

[0582] For these embodiments, a polarizer is placed (for example, nearthe surface to be measured) such that only light passing to and from thesurface passes through it. The polarization axis of the polarizer isplaced at a 45 degree angle to the polarization of the light from thesource such that the light from the surface has a polarization that isat a 45 degree angle from that of the local oscillator light.

[0583] In this situation, a detector module 610 as shown in FIGS. 19Cand 19D may be advantageously employed in place of module 512 of FIGS.17 and 18 and, in modified form, utilizing the same detection principle,for module 576 of FIG. 19A. Elements, in FIGS. 19C and 19D, having thesame function as corresponding elements in FIGS. 17 and 18 are given thesame reference numbers as the elements in FIGS. 17 and 18.

[0584] Module 610 is similar to module 512, except that a quarter waveplate 612 is placed in front of polarizers 516 and 518. The orientationof the polarization of the quarter wave plates, the polarizer and theincident light is shown in FIG. 19D which is a sectional view from belowalong lines D-D in FIG. 19C. The axes of the polarizers are indicated byreference numerals 614, 616 and the polarization axes of the quarterwave plate is indicated by reference number 618. Linearly polarizedlight that is incident on quarter wave plate 612 along one of its axespasses through the plate with its polarization unchanged. Linearlypolarized light having its polarization at 45 degrees to axes 618 istransformed into circularly polarized light.

[0585] Reference numbers 620, 626 indicate the polarizations of theincident grating and surface reflected waves, where, it is immaterialwhich of the two waves is polarized in the direction 620 and which ispolarized in the direction 626. Furthermore, one of the waves may bepolarized in a direction 626′, instead of 626.

[0586] In operation, the incident wave having the polarization 620 istransformed into a circularly polarized wave. This circularly polarizedwave is split into two equal components by polarizers 516 and 518 suchthat two linearly polarized waves of equal amplitude are incident ondetectors 520 and 522. However, these two waves are 90 degrees out oftime phase (as well as having orthogonal polarizations). The wave havingpolarization 626 or 626′ passes through the quarter wave plate withunchanged polarization. It too is split into two waves that haveperpendicular polarization. However, these waves are in time phase. Eachdetector will thus detect the interference between the light waves,which gives rise to two signals that are 90 degrees out of temporalphase. This difference in phase can then be used to determine thedirection as in standard quadrature detection.

[0587] If birefringent plate 612 is omitted, then either the surfacereflection or the local oscillator field is selectively blocked by oneof the detector polarizers, depending on the polarization directions ofthe local oscillator and the reflected surface illumination. If, forexample, the polarization direction of the source is 620, then it willbe blocked by the polarizer referred to by 616. Thus, only the reflectedsurface illumination will be detected by the detector, corresponding tothe E_(r) ² component. Alternatively, if the polarization of thereflected surface illumination is 620, then the detector associated withpolarization direction 616 will detect only the local oscillator field,thereby enabling compensation of the E₀ ² component.

[0588] The output of a detector used for E₀ ² component compensation canbe utilized as a reference voltage and subtracted from the outputvoltage of other detectors used for the translation measurement. Thisforms a kind of ‘differential’ detection mode. For example, suchsubtraction can be performed at the output of the transimpedanceamplifier stage, thus eliminating most of the DC voltage from thedetected signal. Alternatively, a scheme utilizing high-pass filteringto remove the DC voltage, such as described in FIG. 9 may be used.Preferably, the bandwidth of the compensation signal is limitedaccording to the bandwidth of the source noise. Otherwise other,non-correlated noise (e.g., thermal noise), is actually unnecessarilyadded through the subtraction of the compensation signal.

[0589] E₀ ² component compensation is especially useful if the source isturned off and on repeatedly (e.g., when operating in ‘sleep mode’ tosave energy or for eye-safety). A modulated source complicates the DCvoltage elimination with a high-pass such as described in FIG. 9, butthis is reduced or eliminated without a high-pass if E₀ ² componentcompensation is utilized. Alternatively, switching the source may beperformed even without E₀ ² compensation if capacitors in the high-passare isolated when the source is turned off (thereby maintaining theircharge until the source is turned on again).

[0590] Still another use for the E₀ ² component measurement is asfeedback in a source current control loop. This is especially importantin order to control the optical power of the source if significant powervariability is expected (e.g., due to large operating temperaturerange).

[0591] The arrangement of FIG. 19C and FIG. 19D without birefringentplate 612 can be useful when a Vertical Cavity Surface Emitting Laser(VCSEL) is used as the light source. When operated properly, certainVCSEL diodes can have one of two possible orthogonal polarizationdirections, where at any given time the illumination polarization isaligned with one of the polarizations. Thus, an ambiguity exists as tothe polarization direction. This poses a problem in the usage of theVCSEL where direction detection is important, since the two polarizationdirections result in opposite phase difference of cross-polarizeddetector pairs for a given direction of motion.

[0592] According to the configuration presented in FIG. 19D, andassuming the source polarization direction is along 620 or orthogonal to620 (not shown). Then, if the birefringent plate 612 is removed,polarizer 614, for example, will either block or transmit the localoscillator illumination. Thus, detector 522 output will be either highor low, depending on the polarization direction of the source, and thedetector output may be used to control the conversion between therelative phase of the signal and the direction of motion (e.g., as aflag designating the sign of the zero-crossing counting).

[0593] It is sufficient to use one such polarized detector (with high orlow output, depending on the polarization direction) in addition to thedetectors used to detect the motion. However, if two detectors are used(522 and 520) then in each polarization direction one of the detectorswill have high output, while the other will measure the reflectedsurface illumination and may be used for E_(r) ² component compensation.

[0594] In the above scheme, additional detectors are utilized to solvethe polarization ambiguity of a VCSEL. Alternatively, the VCSEL can beslightly rotated with respect to its ‘optimal’ polarization direction.Assuming an ‘optimal’ direction a of the VCSEL polarization such thatthe preferred polarizations are α or α+π/2, then the ratio R_(p) betweenthe DC voltages of detector pairs is: $R_{p} = \left\{ \begin{matrix}{{\tan \quad (\alpha)}:{{one}\quad {polarization}}} \\{{\cot \quad (\alpha)}:{{other}\quad {polarization}}}\end{matrix} \right.$

[0595] Thus, for optimal VCSEL alignment of α=π/4 (along 626, forexample), the DC component detected by the detectors in across-polarized pair such as described in FIG. 19D will be equalirrespective of the polarization direction of the VCSEL.

[0596] However, if $\alpha = {\frac{\pi}{4} + \beta}$

[0597] radians, then R_(p)≅1+2β in one polarization and R_(p)≅1−2β ifthe VCSEL output is in the other polarization. Thus, R_(p)>1 when theVCSEL emits in one polarization and R_(p) is less than one for the otherpolarization. Therefore, if the VCSEL is rotated with respect to the‘optimal’ orientation, the outcome of a comparison between the DCvoltage of detectors in a detector pair used for translation measurementindicates the polarization direction without a need for additional,dedicated detectors for that purpose.

[0598] Still another way to overcome a possible polarization ambiguityof the local oscillator is to use a linear polarizer in the optical pathbetween the source and the grating, with the polarizer axis at 45degrees from either of the orthogonal polarization directions. Thus, forexample, the polarizer is positioned along 620 when the VCSELpolarization is either 626 or 626′. Alternatively, the polarizer ispositioned along 626 if the VCSEL polarization is either along 614 oralong 616. This forces the source polarization to be the same as that ofthe polarizer, at the expense of loss of about half of the opticalpower.

[0599] Low-frequency parasitic noise (such as E_(r) ² and E₀ ²components and power line interference) superimposed on a higherfrequency signal may affect the quadrature detection of thehigh-frequency signal for the following reasons:

[0600] Zero-crossing events of the high-frequency signal are missed.

[0601] The order in which the zero crossing events happen is switched,therefore the direction detection of the quadrature detector isswitched.

[0602] Zero crossing events of the low frequency noise are counted andadded to the measurement.

[0603] One of several approaches (or a combination of approaches) may beused to overcome possible low-frequency modulations by signal processingmeans (in addition or instead of the optical schemes described above),in accordance with various preferred embodiments of the invention:

[0604] Assume P and Q are the output signals of a detector pair such asdetectors 520 and 522 in FIG. 19C. P and Q are ideally identical otherthan a temporal phase difference of +90 degrees or −90 degrees,depending on the direction of motion, and the addition of noise. Assumealso that signals D=P−Q and S=P+Q are derived from signals P and Q.Then, signal D has the property of elimination of all noise sources thatare common to both P and Q. Moreover, D and S have 90 degrees temporalphase difference. Therefore, D and S are equivalent to P and Q whenthere is no noise, but if common noise sources are significant, D zerocrossings accurately measure the translation while zero crossings of Scan be utilized to aid in determining the direction of motion.Furthermore, the elimination of common noise is not restricted to lowfrequencies.

[0605] The amplified signal may be divided to two (or more) frequencyranges. Selection of the appropriate channel may be based on themeasured frequency.

[0606] Use an adaptive band-pass, controlled by the signal frequency andcapable of adapting to the frequency changes resulting from possibleacceleration of the surface relative to the OTM component. Adaptiveband-pass also reduces other sources of noise, such as thermal noise and1/F noise. It may be implemented, for example, by usingvoltage-controlled capacitors in the high-pass and low-pass elements.

[0607] Use higher amplification of the high-frequency signals, such thatthe resulting amplitude of the high frequency signal is higher than thatof the low-frequency, and so the high-frequency zero crossings count isonly mildly affected.

[0608] A preferred embodiment of an adaptive band pass circuit 899 forthe rejection of low frequency noise in the presence of a high frequencysignal is presented in FIG. 27. A zero-crossing detector 900 converts ananalog signal at an input 910 to a logic signal at an output 920. Whenthe signal is at low frequency (e.g., 50 Hz), transistors 931 and 932are not conducting most of the time, and a capacitor 940 is chargedthrough a resistor 945 with a long time constant (0.1 sec), appropriatefor the detection of the low frequency signal. On the other hand, whenthe zero crossing rate is high (above a few hundred Hertz), a high passcircuit 950 drives current through the bases of transistors 931 and 932,so that capacitor 940 is charged through a resistor 960, with a timeconstant as low as 0.1 msec. Thus, the threshold at the positive inputof an operational amplifier 970 follows the low-frequency noise andthereby rejects its detection, and the operational amplifier output isdetermined by the high frequency signal. A capacitor 980 is used tosuppress spontaneous oscillations of operational amplifier 970. Itshould be noted that FIG. 27 presents one typical implementation of thisaspect of the invention, and the adaptive zero crossing detector can beimplemented in numerous ways and using other components (e.g., FETtransistors, different resistance and capacitor values and a differentoperational amplifier).

[0609] Quadrature motion measurement relies on measuring two identicalsignals, having a constant phase shift between them. Motion magnitude isdetected by the number of zero crossings in a given interval. Motiondirection is determined by comparing the sign of the zero crossing onone channel (i.e., ‘low to high’ or ‘high to low’) to the sign of thesignal in the other channel (‘high’ or ‘low’).

[0610] Noise on the quadrature signal can result in additional zerocrossing counts. If two zero crossings of one signal occur while theother signal did not change sign, their directions are opposite and theyadd to zero. However, if a zero crossing on one signal is shifted intime, the order in which the zero crossings in the two channels occurmay be reversed and result in direction detection errors in bothchannels, that adds up to a net count error.

[0611] Errors due to reversed zero crossing events can be corrected,according to some preferred embodiments of the invention, using‘majority voting’ over some interval. It is assumed that the motiondirection is unchanged within each interval (or ‘cell’). This means thatthe resolution is compromised for enhanced accuracy. Conveniently, thezero-crossing counting process is performed in contingent cells. Eachcell starts at the end of the previous cell and ends when a predefinednumber of zero-crossing events or more has happened in both quadraturechannels. Then, the direction for all the cell is determined accordingto the majority of direction determinations (in both channels or in oneof them only) in that cell. Preferably, each cell represents a fixednumber of counts, irrespective of the actual number of counts in bothchannels (thus, the resolution is degraded by twice the number ofminimum counts in the cell). Conveniently, a cell of size 3 or 4 may beused. The requirement that both channel counts equal or exceed theminimum number of a cell is intended to prevent high-frequency noise inone channel from ‘taking-over’ the majority voting.

[0612] In an optical translation measurement of many of the typesdescribed above, according to some preferred embodiments of theinvention, the detector DC voltage resulting from the local oscillatorenergy is conveniently removed using a high-pass at the output of afirst amplification stage before further amplification of the AC signal.Therefore, the high-pass cut-off frequency determines the minimummeasurable velocity.

[0613] When optical translation measurement is used for an input device(such as a mouse or other pointer device), the low-velocity limitationmay be an important factor for the user, e.g.—when the user slows themotion and approaches a specific position on the screen.

[0614] In order to enable the user to slowly move the cursor so that itcan be positioned with high accuracy on the screen, a moderate (ratherthan a sharp) high-pass filter may be used. Using a gradually decreasingamplification slope with frequency will result in missed zero-crossingsclose to the filter cut-off. This will effectively reduce the measuredvelocity as the velocity approaches the lower limit set by the filter.Thus, the cursor velocity is gradually reduced to zero while the OTM isstill within the measurement bandwidth (and still moving). This‘deceleration’ mechanism may also be applied in software or as part ofthe signal analysis following the zero crossing detection, by measuringthe count rate (i.e.—velocity) and reducing the cursor velocity when thecount rate approaches the filter lower limit. In a preferred embodimentof the invention the cut off frequency is equivalent to a motion of lessthan about 0.5 mm/sec. In a preferred embodiment of the invention, thehigh pass filter has a slope, below the cut off frequency of less thanabout 20 db/octave.

[0615]FIG. 23 shows an ideal curve 750 of cursor velocity as a functionof device velocity. FIG. 23 also shows a curve 752 of cursor velocity asa function of device velocity, in accordance with a preferred embodimentof the invention. Also shown, is a curve 754 which would result if arelatively sharp high pass filter were used. As can be understood, curve754 results in a virtual inability of the system to move a cursor at aslow speed. On the other hand, the ideal curve is not achievable, sincezero and low frequencies must be excluded. However, the gradualtransition of curve 752 allows for an accurate placement of the cursor,using a non-linear transfer function. In an exemplary device, curve 752could be linear down to some value, such as for example, 1 mm/sec andcause no movement of the cursor for hand (device) velocities lower thanone-third to one half of the minimum linear velocity. Of course adifferent curve could be used, having an even smoother transition.

[0616] The accuracy of optical translation measurements, as describedabove, depends on the number of grating lines in the illuminating beam.Thus, for high-curvature surfaces, a planar optical configuration maynot be accurate enough. An example of such an application is themeasurement of the rotation of a shaft 600, as illustrated in FIGS. 20Aand 20B, where the shaft radius may be small. For the measurement ofshaft rotation, a device can be placed along the shaft (on the side ofit). To accommodate the shaft curvature and enable measurement of smalldiameter shafts, a special optic 602 can be used as the front-end of thedevice component. The shape of the optic is shown schematically in FIGS.20A and B. The diameter of the optic is matched to the shaft diameter,and the surface of the optic is patterned with a one-dimensional grating604 whose lines are parallel to the shaft axis. A source light 606 isdirected to focus at the center of the shaft, so its phase is constantacross the grating. Preferably, the measurement is a 0^(th) order type.A detector 608 detects the light reflected from the surface of the shaftand the light reflected from the grating. Note that, preferably, thesource and detector are at the circumferential position with respect tothe shaft but are axially offset from each other as shown most clearlyin FIG. 20B.

[0617] The front-end optic can be changed for different shaft diameters,and allows high-resolution measurement by looking at a substantialportion of the shaft circumference. Direction detection can be obtainedby using an asymmetric grating, or by means of another portion of thelight that will be focused onto the shaft surface and detect directionby the orthogonal polarization method described above, or by other means(e.g.—observing the motor driving current polarity). An advantage ofusing the arrangement of FIGS. 19A or 19B is in equalizing the pathlength of the local oscillator and scattered radiation, while using thesame portions of the beam for both.

[0618] Motion parallel to a rough surface may induce inadvertent Z-axis(up and down) motion as well. The Z axis motion induces a Doppler shiftof the radiation reflected from the surface, and, in general, the phaseof the radiation will change in response to a combination of Z and X orY velocities. A way to decouple the relative contributions is to usemeasurements in both the +1 and −1 diffraction orders (or othersymmetric orders, such as ±2, ±3, etc.) for each of the X and Y axes.Looking at the geometry of an incident wave perpendicular to themeasured surface, velocities v_(X) and v_(Z), source light wavelength λ,and grating line spacing Λ, the Doppler frequency shift for combined Xand Z motion, as measured at the +1 order, is:

ω₊=(2π/λ)(v_(X)sin(φ)−v_(Z)(1+cos(φ))), where sin(φ)=λ/Λ.

[0619] A measurement at the −1 order will result in a Doppler shift of:

ω⁻=(2π/λ)(−v_(X)sin(φ)−v_(Z)(1+cos(φ))).

[0620] We can see that a signal oscillating at the difference of the twofrequencies will have: ω₊−ω⁻=(4π/Λ)v_(X), while the sum frequencyresults in ω₊+ω⁻=(4π/λ)v_(Z)(1+cos(φ)).

[0621] Taking two quadrature signals for the two orders we have thefollowing signals:

A ⁺=cos(ω₊ t+Φ ₊), B ⁺=sin(ω₊ t+Φ ₊), A ⁻=cos(ω⁻ t+Φ ⁻), B ⁻=sin(ω⁻ t+Φ⁻).

[0622] Using sin and cos summation rules we can form combinations thatwill both oscillate at the sum or difference frequencies, and maintainquadrature relations:

C−=B ⁺ A ⁻ −A ⁺ B ⁻=sin(ω₊ t−ω ⁻ t+Φ ₊−ω⁻),

D ⁻ =A ⁺ A ⁻ +B ⁺ B ⁻=cos(ω₊ t−ω ⁻ t+Φ ₊−Φ⁻),

C ⁺ =B ⁺ A ⁻ +A ⁺ B ⁻=sin(ω₊ t+ω ⁻ t+Φ ₊+Φ⁻),

D ⁺ =A ⁺ A ⁻ −B ⁺ B ⁻=cos(ω₊ t+ω ⁻ t+Φ ₊+Φ⁻).

[0623] The resulting signals C⁻, D⁻, have thus decoupled the relativecontributions and eliminated the spurious Z axis contribution to the Xaxis measurement. Additionally, the + component can be used specificallyfor Z axis measurement only, for example for touch or ‘click’ detectionin a touch point, without measurement of the zeroth order diffraction

[0624] When the Z-axis velocity is relatively high, each of the X-Ymeasurements can usually be used also as a crude estimate for the Z-axistranslation. Thus, the ‘down-and-up’ characteristic of the ‘Click’operation of a finger can be detected. Also, it is possible to detectthe ‘Click’ operation using the abrupt deceleration and acceleration bythe finger on touching and detaching from the touch-point, respectively.For the latter, only the absolute Z-axis velocity (or it's derivative)is used.

[0625] Another methodology for the determination of Z-axis translationand the accurate determination of transverse motion is illustrated withthe aid of FIG. 21. FIG. 21 shows part of a system 700 in which twodetector pairs, a Z-detector 702 and an X-detector 704 are used todetermine both Z and X directed motion. In preferred embodiments of theinvention, the Z-detector and the X detector each consist of a pair ofcross-polarized detectors, such as those shown in FIGS. 19C and 19D andas element 512 in FIG. 18 and element 576 on FIGS. 19A and 19B. Thesurface has both x and z directed velocity (with respect to thedetection system). The overall velocity is shown as the vector V (V_(Z)in the normal direction and V_(X) in the parallel direction) on FIG. 21.

[0626] Z-detector 702 is preferably situated so that it receives Dopplershifted energy from surface 12 including only frequency shifts based onZ-motion (the light source, which is not shown, is assumed to benormally incident on the grating). X-detector 704 is so situated that itreceives (for example) first order diffraction from the grating andDoppler shifted reflections from surface 12 at an angle φ with respectto the normal. The Doppler shifted reflections of the X-detector isbased on a combination of the Doppler shifts of the X and Z directedmotion of the surface with respect to the detectors.

[0627] Let U_(X) be the component of the velocity along the bisectorbetween the zero order and the first order. Then:

U _(X) =V _(X) sin(φ/2)+U _(Z) cos(φ/2).

[0628] The Doppler effect creates a frequency shift measured in the Xand Z detectors, respectively:

F _(X)=2U _(X) cos(φ/2)/λ, and

F _(Z)=2U _(Z)/λ.

[0629] The velocity along X axis, V_(X), can be determined from themeasurable quantities F_(X) and F_(Z) by combining the above relationsto:

V _(X) =λF _(X)/sin(φ)−λF _(Z) ctg(φ/2)/2.

[0630] If the first grating order is used, then sin(φ)=λ/Λ, where Λ isthe grating line spacing. Thus:

V _(X)=Λ(F _(X) −F _(Z) cos²(φ/2)).

[0631] When φ is small, cos²(φ/2)˜1, simplifying the Z decoupling:

V _(X)=Λ(F _(X) −F _(Z)).

[0632] For determination of X and Y motion, three detectors are used asshown in FIG. 22A which shows the detectors at the focal plane of system700.

[0633] If more accurate decoupling is required, a separate zero orderdetector may be used. By deflection of a small portion of theilluminating beam in an angle of φ/2, the new zero order from thedeflected beam measures only Z-axis motion, but the Doppler frequency isnow multiplied by 1+cos(φ)=2 cos²(φ/2), i.e.—it will exactly match theZ-axis motion coupling to the X and Y axis measurements, enablingprecise decoupling of it.

[0634] In an alternate preferred embodiment of the invention, it is alsopossible to decouple the effects of X and Z directed motion using onlynon-zero order reflections. This may be desirable since it avoidsdetection at near zero frequencies.

[0635] Assuming, for simplicity of exposition only, normal illumination,three detectors i=1 . . . 3 are used, each representing a gratingspacing of Λ_(i), and are positioned at angles γ_(i) with respect to theX axis in the X-Y plane. Therefore, the detectors measure the number ofcycles, N_(i) of a pseudo-sinusoidal signal according to:

N _(i)=1/Λ_(i)(X cos(γ_(i))+Y sin(γ_(i)))+1/λ·Z(1+cos(φ_(i))),

[0636] where X and Y are the translations along the X and Y axes,respectively, Z is the translation component along the normal to theplane, λ is the source wavelength and φ_(i) is the i-th detector anglewith respect to the illumination direction in the reflection plane, andis related to Λ_(i) as:

sin(φ_(i))=λ/Λ_(i).

[0637] If, for example, one detector is on the X axis (γ₁=0), another ison the Y axis (γ₂=π/2) and the third is at 45° to the others (γ₃=π/4),then: $\begin{matrix}{N_{1} = {\frac{X}{\Lambda_{1}} + {\frac{Z}{\lambda}\left( {1 + {\cos \quad \varphi_{1}}} \right)}}} \\{N_{2} = {\frac{Y}{\Lambda_{2}} + {\frac{Z}{\lambda}\left( {1 + {\cos \quad \varphi_{2}}} \right)}}} \\{N_{3} = {{\frac{\sqrt{2}}{2} \cdot \frac{X + Y}{\Lambda_{3}}} + {\frac{Z}{\lambda}\left( {1 + {\cos \quad \varphi_{3}}} \right)}}}\end{matrix}$

[0638] The following approximation can be taken:

1+cos φ₁=1+cos φ₂=1+cos φ₃ ≡k _(z).

[0639] Also, if a simple 2-D grating with a square unit cell is used(see FIG. 22B), then (assuming also small φ angles):

Λ₁=Λ₂≡Λ

Λ₃≅Λ/{square root}{square root over (2)},

[0640] where Λ₃ stands for the first order at 45° from the X axis. InFIG. 22B, element 710 is the Y first order detector; 712 is the X firstorder detector and 714 is the X+Y first order detector.

[0641] Substitution and rearrangement lead to the expressions for X, Yand Z: $\begin{matrix}{X = {\Lambda \left( {N_{3} - N_{2}} \right)}} \\{Y = {\Lambda \left( {N_{3} - N_{1}} \right)}} \\{Z = {\frac{\lambda}{k_{z}}\left( {N_{1} + N_{2} - N_{3}} \right)}}\end{matrix}$

[0642] It is evident that the translation in X and Y is measured at thetwo detectors not lying on the measured axis. This eliminates the Z axiscoupling and at the same time enables much better resolution in caseswhere the motion direction is close to the perpendicular to one of theprimary axes.

[0643] Another example is similar to the latter, but when Λ₃ is doubled:

Λ₁=Λ₂≡Λ

Λ₃≅2Λ/{square root}{square root over (2)}

[0644] This configuration is equivalent to one detector on the X axis, asecond on the Y axis and the third half-way between them (see FIG. 22C),so that the three detectors form a straight line. In FIG. 22C, 714′indicates the (X+Y)/2 combined order detector. This configuration ispreferable for manufacturing purposes (especially considering thebeam-splitting used for direction detection using the static phaseshift). It is also easily obtainable with a dedicated 2-D phase-grating.

[0645] To convert to translation along the axes in this case:$\begin{matrix}{X = {\Lambda \left( {{2N_{3}} - N_{2}} \right)}} \\{Y = {\Lambda \left( {{2N_{3}} - N_{1}} \right)}} \\{Z = {\frac{\lambda}{k_{z}}\left( {N_{1} + N_{2} - {2N_{3}}} \right)}}\end{matrix}$

[0646] Still another possible configuration is when one detector (720)is on the X axis and two others (722 and 724) are symmetricallypositioned relative to it, i.e.—γ₁=0;γ₂=γ;γ₃=−γ and Λ₁≡Λ_(x);Λ₂=Λ₃≡Λ_(y)(see FIG. 22D).

[0647] Assuming again that 1+cos φ₁=1+cos φ₂=1+cos φ₃≡k_(z):$\begin{matrix}{N_{1} = {\frac{X}{\Lambda_{x}} + \frac{k_{z}Z}{\lambda}}} \\{N_{2} = {{\frac{1}{\Lambda_{y}}\left( {{X\quad \cos \quad \gamma} + {Y\quad \sin \quad \gamma}} \right)} + \frac{k_{z}Z}{\lambda}}} \\{N_{3} = {{\frac{1}{\Lambda_{y}}\left( {{X\quad \cos \quad \gamma} - {Y\quad \sin \quad \gamma}} \right)} + \frac{k_{z}Z}{\lambda}}}\end{matrix}$

[0648] The following selection is conveniently (but not necessarily)made so that the X and Y resolutions will be identical:$\Lambda_{x} = \frac{\Lambda_{y}}{{\sin \quad \gamma} + {\cos \quad \gamma}}$

[0649] Therefore, defining:${k \equiv {\frac{1}{\Lambda_{X}} - \frac{\cos \quad \gamma}{\Lambda_{y}}}} = \frac{\sin \quad \gamma}{\Lambda_{y}}$

[0650] and rearranging:

X=1/2k(2N ₁−(N ₂ +N ₃))

Y=1/2k(N ₃ −N ₂)

[0651] Here again, the Z axis is decoupled, and also the resolution ishigh even in near-perpendicular motion to any of the primary axes.

[0652] Furthermore, for a convenient extraction of the Z axistranslation, y is set to tan(γ)=2, so:$Z = {\frac{\lambda}{k_{z}}{\left( {{2N_{1}} - \frac{N_{2} + N_{3}}{2}} \right).}}$

[0653] Any of the detector arrangements can be the product of a single2-D grating (though in general it will not be composed of an array ofrectangular unit cells), or by using two or three separate gratings,preferably illuminated by different portions of the initial beam, eachcontributing a local oscillator to only one or two detectors.

[0654] It should be noted that while FIGS. 22A, 22B and 22C show asingle detector for each of the orders of diffraction, in fact, eachconsist of a pair of cross-polarized detectors, such as those shown inFIGS. 19C and 19D and as element 512 in FIG. 18 and element 576 on FIGS.19A and 19B.

[0655] The total power of a source used in devices of the invention isgenerally not high. However, it may be desirable, in some preferredembodiments of the invention, to provide for an eye safely mechanism toreduce the chances of the laser inadvertently hitting the eye of a user.In a preferred embodiment of the invention, an additional detector isprovided which is positioned to receive light reflected from thesurface, without at the same time receiving light reflected or refractedfrom the grating. This is easily achieved by placing the additionaldetector between the zeroth order diffraction and the first orderdiffraction beams or any other orders. Conveniently, this detector mayalso be used simultaneously for E_(r) ² component compensation, asdescribed above. For example, the additional detector may be placedbetween elements 34 and 40 in FIGS. 3A, 3B or 3C; and in analogouspositions in other embodiments described above.

[0656] Light will be incident on the additional detector and thedetector will produce a signal only when an object (other than thegrating) is positioned to reflect light to it. Thus, if neither asurface or a finger or other object blocks the beam (and thus reflectslight back to the additional detector), it will not produce a signal.

[0657] In accordance with a preferred embodiment of the invention, thesource is turned off whenever the light detected by the additionalsensor falls below some threshold value. Periodically, for example,every 100 msec, the source is turned on again for a very short time tocheck if light is incident on the additional detector. If it is, thesource is kept on and the device measures motion, if any exists. If noor low incident light is detected, the source is extinguished for anadditional period. This process is repeated until the a light signalabove the threshold value is detected at the additional detector.Preferably, hysteresis is introduced on the threshold to preventparasitic oscillations.

[0658] Alternatively or additionally, when no motion is detected for apredetermined period, for example, for one or a number of minutes, themotion detector goes into a “sleep mode.” In the sleep mode the sourceis extinguished except for short periods (for example 50 or 100milliseconds in every second or every half second). If during the “on”period, motion is detected, the motion detector switches to normaloperation.

[0659] The present invention has been described in conjunction with anumber of preferred embodiments thereof which combine various featuresand various aspects of the invention. It should be understood that thesefeatures and aspects may be combined in different ways and variousembodiments of the invention may include one or more aspects of theinvention. The scope of the invention is defined by the following claimsand not by the specific preferred embodiments described above. As usedin the following claims, the words “comprises”, “comprising”,“includes”, “including” or their conjugates shall mean “including butnot necessarily limited to”.

1. A method for determining the relative motion of a surface withrespect to a measurement device comprising: placing a partiallytransmitting object, which is part of the measuring device, adjacent tothe surface; illuminating the surface with incident illumination, whichdoes not constitute an interference pattern, such that the illuminationis reflected from portions of the surface, wherein at least part of atleast one of the incident and reflected illumination passes through theobject; detecting the illumination reflected from the surface, andgenerating a detected signal; and determining the relative motion of thesurface parallel to the surface, from the detected signal.
 2. A methodaccording to claim 1 and comprising: varying the phase betweenillumination reflected from or diffracted by the object and at least aportion of the illumination reflected from the surface.
 3. A methodaccording to claim 2 wherein the direction is determined based on saidvaried phase.
 4. A method according to claim 1 and including determiningmotion in a direction perpendicular to the surface.
 5. A methodaccording to claim 1 wherein varying the phase comprises periodicallyvarying the phase.
 6. A method according to claim 5, wherein determiningthe direction of relative motion comprises determining the direction ofrelative motion based on a characteristic of the signal caused by saidperiodically varying relative phase.
 7. A method according to claim 2wherein varying the phase comprises: causing the object to moveperiodically substantially in the direction of the motion beingmeasured.
 8. A method according to claim 2 wherein varying the phasecomprises: causing the object to move periodically substantiallyperpendicularly to the direction of the motion being measured.
 9. Amethod according to claim 2 wherein varying the phase comprises:providing a transparent material between the object and the surface; andelectrifying the material such that its optical length in the directionof the illumination varies.
 10. A method according to claim 9 whereinthe transparent material is a piezoelectric material.
 11. A methodaccording to claim 1 and including determining both the magnitude anddirection of the translation utilizing a single detector.
 12. A methodaccording to claim 2, wherein varying the phase comprises, introducing astatic phase change and wherein determining the direction of relativemotion comprises determining the direction of relative motion based on acharacteristic of the signal caused by said phase change.
 13. A methodaccording to claim 2 and including: dividing at least part of theillumination that is reflected from the surface into at least a firstillumination having a first phase and a second illumination having asecond phase.
 14. A method according to claim 13 wherein said first andsecond illuminations have different polarizations.
 15. A methodaccording to claim 14 wherein dividing comprises passing theillumination incident on the surface through a birefringent material.16. A method according to claim 14 and including passing theillumination reflected from the surface through a birefringent material.17. A method according to claim 15 and including placing thebirefringent material between the object and the surface.
 18. A methodaccording to claim 1 and including determining the magnitude anddirection of the translation utilizing two detectors which producedifferent detected signals depending on the direction of thetranslation.
 19. A method according to claim 18 and includingdetermining the direction of translation from the sign of a phasedifference between the different detected signals.
 20. A methodaccording claim 1 wherein the illumination is perpendicularly incidenton the surface.
 21. A method according to claim 1 and includingdetermining the direction of motion.
 22. A method according to claim 1wherein determining the motion comprises determining variations in theamplitude of the signal with position.
 23. A method according to claim22 wherein the motion is determined from zero crossings of the detectedsignal.
 24. A method according to claim 1 wherein the surface is anoptically diffusely reflecting surface.
 25. A method according to claim1 wherein the surface has no markings indicating position.
 26. A methodaccording to claim 1 wherein the illumination comprises visibleillumination.
 27. A method according to claim 1 wherein the illuminationcomprises infra-red illumination.
 28. A method according to claim 1 andincluding detecting relative motion of the surface in two directionsparallel to the surface.
 29. An optical mouse comprising: a housinghaving an aperture facing a surface; and an optical motion detectorwhich views the surface through the aperture, wherein the optical motiondetector utilizes the method of claim 1 to determine the translation ofthe housing with respect to the surface.
 30. A touch point device foruse as a control device, comprising: a housing having an aperture; andan optical detector which determines the motion of a finger which istranslated across the aperture wherein the optical detector utilizes themethod of any of claim 1 to determine the translation.
 31. A combinationmouse/touch point for use as a pointer for a computer comprising: ahousing having an aperture; an optical detector which determines themotion of an object which is translated across the aperture; and meansfor determining whether the aperture is upward or downward facing.
 32. Acombination mouse/touch point according to claim 31 wherein the opticaldetector utilizes the method of claim 28 to determine the translation.33. An encoder comprising: an optically diffusely reflecting surfacehaving no markings other than reference markings; and an opticaldetector having relative motion with respect to the surface, wherein theoptical detector measures relative motion with respect to the surfacerelative to the reference markings, wherein the optical detectorutilizes the method of claim
 1. 34. An encoder according to claim 33wherein the surface is the surface of a disk which rotates about an axisand wherein the detector measures the rotation of the disk.
 35. Avirtual pen comprising: an optical detector which is adapted to measurerelative motion with respect to an optically diffuse surface utilizingthe method of claim 1; and circuitry which translates said measuredrelative motion into written or graphical data.